AD/A-000 997

HEAT CIRCUITS OF THERMOELECTRICDEVICES

G. K. Kotyrlo, et al

Army Foreign Science and Technology CenterCharlottesville, Virginia ý

19 July 1974

DISTRIBUTED BY:.••

NI*Wmam Techmical WKInfGmN SffkvbU. S. DEPARTMENT OF COMMIERICE

S.A

DEPARTMENT OF THE ARMYU.S. ARMY FOREIGN SCIENCE AND TECHNOLOGY Z;ENTER 1:E I~2340 SEVENTH STREET NE.

C4ARLOTTESVILLE, VIRGINIA 22301

TRANSLATION

In Reply Refer to:IS3( HT-23 853-74I)IA Tas No. T741801 Date: 19 July 1974

~~ INGLISH rrrLE: Heat Circuits of Thermoelectric Devices

S0O.!CW: "Naukova Dumka", Kiev, 1973. Ukrainian SSR Academy of Sciences

08PDA1911IOt: Kotyrlo, G. K. Shchegolev, G. M.

I.ANGL:'A(;E.: Russian

(.OINTrRy: USSR '

REQU'EST(-R: GE - Turner

TIRANSLATOR: Leo Kanner Associates [MAC]

ABSTRACT. N

A general discussion of thermoelectric devjices is followelby a-' detailed mathematical analysis of the efficiency,temperature fields at the thermocouple junctions, thepower level, etc. of various electrical power generatorand refrigerator configurations. Single and two-stagedesigns of these devices are analyzed both qualitativelyand quantitatively. A basic contrast between permeable Iand monolithic thermocouples is extensively developed

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TABLE OF CONTENTS

,.o.ewor. .. ... ... ........................ . . . . . 2

The Fundamental Heat Circuit Elements of Thermoelectric

Devices . . .. .. . . . . . . . . . . . . . . . . . 4

1. Heat Sources . ............... 5

2. Heat Delivery and Dissipation Systems . . . 16

3. Power Sources ............... 28

Chapter II

The Classification of Heat Circuits of Thermoelectric •- -i

Devices ....................... . 31 4

1. Generator Circuits ...... .. . .... 31

2. Circuits of Refrigerators, Conditioners

and Heat Pumps .............. 55 L -

Chapter II

Features of Temperature Fields in Permeable

Thermocouples...... . ... ........... . 60 I

1. Method of Calculating the Ternperature Fields 63

2. Analysis of the Temperature Fields . . . . . 70 IChapter IV

The Design of Thermoelectric Generators with

Permeable Thermocouples .... ............... 74

1. The Design of a Generator Flushed by a

Coolant Flowing from the Cold to the Hot

Junctions ................ . . . . 75

2. Design of a Generator Where the Heat

Carrier Blows Through from the Hot to theCold Junctions .............. 95

3. Two-stage Generator Design . ....... 109Chapter V

Thermoelectric Cooling Devices with Permeable

Thermocouples .................... . 117

1. Refrigerator Uesign Method . . . . . . . . 118

2. An Operational Analysis of a Cooling Device 125

Conclusion . .. .. .. .. .. .. .. .. .. .. . .. 130 '

Bi bliJography . . . . . . . . . . . . . . . . . . . . . . .133 •

- "' -

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0

3i

FOREWORD

Thermoelectric devices have such valuable qualities as silent operation,

reliability, the capability 'of operating for an extended period without

servicing, compactness, and they are self-contained. It is just these qual-

ities which explain the rather wide application of thermoelectric devices .

as well as which delineate the areas of their maximum distribution at the

present time: powering the devices in space equipment, radio and meteor-

ological stations, sea navigation buoys and various devices for ground and

water transport, cathodic protection of piping and metallic instailations.

The wider introduction of thermoelectric devices, in particular in I

stationary power engineering, is held back by their comparatively low power

efficiency and the high cost per kilowatt. Because of this, a large number

of laboratories and scientific organizations of the Soviet Union ana many

foreign countries are intensively carrying out investigations into the processes

which take place during the operation of thermoelectric devices, and are

-2-

developing new semiconductor thermoelectric materials. Even more efficient

and economical devices are being created as a result.

Efforts to increase the efficiency of thermoelectric devices are basically

directed towards finding new materials with a high thermoelectric figure of

merit z = 2 I/°K, the refinement as well as the development of the

process engineering for interconnecting thermoelectric modules and for more

effective heat transfer to the hot and cold surfaces of thermoelectric

batteries, which assure minimal temperature losses, i-.e. the finding of methodsof effectively interlinkin- batteries with hot and cold heat sources.

Insufficient attention has been given to the development of new, more

refined heat circuits and the analysis of their influence on the power

efficiency of theri-celectric devices.

An attempt is made in the present work to consider the heat circuits

of thermoelectric devices from the point of view of their thermodynamic

efficiency, and evaluate the possible influence of the choice of heat circuit

on the power efficiency of the batteries. It is interesting from this view-

point to also consider thermoelectric batteries in which the primary quantity

of heat is suppliee or removed not through the surfaces of the hot and cold

junctions, but within the thermocouples. Thermocouples are considered whose

branches are made permeable to a substsnce being cooled when the battery is

operated in a refrigerator mode, or a heat carrier (coolant) when operated as

a generator of electrical power.

In permeable thermocouples, the internal heat exchange surface can be t

quite developed, a consequence of which is tne fact tho tri he heat exchange

fbetween the gas (liquid) passing through it and the sold material occurs at

bsmall temperature differences, i.e. almost reversibly. Such a heat exchange

3 -

system is responsible fo.,, the fundamental and essential features of thermo-

couple operation. In particular, new possibilities of Influencing the cool-

ing coefficient of a thermnoelectric b.ttery or its efficiency when operating

in a generator node are opening up.

Chapter I

The Fundamental Heat Circuit Elements of Thermoelectric Devices

The heat circuit of any thermoelectric device contains the usual common

basic components irrespective of its function. A thermoelectric battery

operating in any mode should have a hot and cold heat source, systems for

delivering heat from the hot source to the hot junction and removing it fromn

the cold junction to the cold sink, as well as an internal load which the

battery powers in a generator mode, or an external power source when operating Iin refrigerator or heat pump modes.

Considering the existing battery design, it should be noted that they are

basically made up of thermocouples of a rectangular shape and in a smaller

number of designs, of ring-shaped ther~mocouples. More rarely employed are

trapezoidal, cubic and other shapes which are chosen in the design of thervo-

electric devices solely from considerations of connection convenience and

operational peculiarities, since ,-ither the shape nor the geometric dimensions

of thermocouples exhibit an influence on the battery efficiency.

The main difficulties in making batteries are caused by the necessity

of electrically connecting a significant number of p- and n- type elements.

-4 - N1

9. 9 SA

However, there is no necessity to make up high power batteries by connecting

the semiconductor materials in a series parallel configuration. Simpler and

more reliable is the fabrication of batteries of any power from individual

modules, which take the form of a few interconnected thermoelectric couples.

Such low-power thermoelectric modules make it possible to fabricate a battery

of any construction and power with the high reliability of series parall,.,

connection.

Multistage thermocouples can also be analogously interconnected in low

power modules. Many works [5, 16, 24] have been devoted to the technological

questions of fabricating p- and n- type branches, their interconnection in

thermoelectric modules and structural layout, so there is no point in going

into these questions in detail.

We will consider in greater detail the other common circuit elements of

thermoelectric devices which play an active part in the operation of the heat

circuit and give it its characteristic features.

1. Heat Sources

One of the primary heat circuit components of thermoelectric generators

is the source of heat energy, whose choice is of considerable significance in

the design of the generator depending on the required length of its continuous

operation, its function, useful electric power, etc.

The basic heat sources in generators already constructed at the present

time and those being designed are combustion products of chemical fuels,

radiant energy from the sun, radioisotopes, and nuclear reactors.

5

S~-5-

__-Chemical fuel is used primarily as a heat source in generators for

ground service, which arv' emp,(.yed for powering radio equipment, lighting,

and the cathodic proteen'on of metallic installations and piping which are

located in difficult access regions.

in t*.ansport installc'ions, where the dimenisions and weight of the power

suppl-; system play a determining par t , the use of a chemical fuel is in- 43

expe•:,:t ir the liajority .Jf cases since a large quantity of fuel is required

to as,,.-- an exter, '.d -9riod of geneiator operation.

I. developti;, -..at source us-ng chemical fuel, primary attention isgiven to the cor,.ruction of the burner device and the selection of an optimum

"combustiun chamber shape from the point of view of the orgnization of the burn-

.ing process. The burner device and the combustion chamber should assure the

requisite heat flow dEnsities at the given hot junctien temperature and a max-

imum completeness of fuel combustion. When high temperature thermoelectric

materials are employed in the manufacture of the thermocouple branches, the

solution of this problem can occasion substantial difficulties.

In principle, aoy types of chemical fuels can be used in thermoelectric

devices - liquid, solid and gaseous. The working substances ef various

thermal cycles (steam, hot water, exhausted combustion products) can likewise

be used a heat source. In this case, the gener.itor can be located at the

most diverse points in the heat circuit of any heat-consuming installation.

Where the waste heat from the working substances of thermal cycles or the

exhaust gases from plants operating on the combustion products of organic

fuels is utilized to obtain electrical energy, such generators will promote

an Increase in the power efficiency of the basic cycle.

6

-6

Radiant energy from the sun is a promising and, in particular cases,

inexpensive heat source for generators for space vehicles and ground service,

which are located in meteorologically favorable regions of the earth.

The conditions favorable for generator operation are determined by the

number of hours of sunshine and the total radiation reaching the surface of

the earth in the given region W3).

The utilization of radiant energy from the sun as the sole heat source

for a generator under space flight conditions is still rather complex and ex-

pensive. This is explained by the complexity and high cost of devices for

focusing solar radiation, which create the heat flow densities necessary for

normal generator operation, or of collectors, which absorb radiant energy, by

the complexity of the devices for tracking focusing systems with a luminary

when the space vehicle is rotating, and by the necessity for utilizing storage

batteries during the time when the space vehicle is in the shade of the earth

or another planet. However, solar converters for operation on board a space

ship, operating at specified distances from the sun, at the present time already

have an advantage in cost, weight per unit power, and reliability over systems

with photoelectric elements, systems with a turbogenerator having a nuclear

reactor heat source, etc. Such restIts were obtained in the comparison of

various means of generating elect. ical power for converters ha'ing a useable

power of up to 100 kw [29].

An interesting direction in the efforts to create solar generators for

space service, the successful development of which will increase even more

the role played by converters of this type, is the development and creation

of heat batteries, which provide for the normal operation of the generator

whilE the space vehicle is located in a shadow. The use of prinmarily lithium

-7-

fluoride and hydride is proposed for the heat-storing materials [32].

In the creation of solar generators for ground service, primary attention

is devoted to the development of devices for focusing solar radiation withr4systems for daily tracking and yearly declination. A significant number of

concentrator designs have been built and tested at the present time. Install-

ations using a system of independent heating of each thermocouple from a

separate reflector and with large diameter parabolic reflectors working on a

group of thermocouples have been tested. Various systems if solar receivers

which convert the radiant energy coming from the reflectors into heat energy

have been developed [l].

Radioisotope heat sources have recently found wide application in the

creation of generators for various purposes. The utilization of the heat

which is emitted during radioisotope decay to heat the hot junctions of a

generator makes it possible to create a reliable, self-contained, and com-

paratively long service life system of energy supply for application in space

vehicles and operation on sea and land. In spite of the fact that radio-

isotope sources cannot provide for large heat flow densities, they are ideal

heat sources for low power generators (ten3 and hundreds of watts), since

they are small and simple to fabricate.

Radioisotope sources, in contrast to other heat sources, are suitable

for application in thermoelectric installations and are characterized by a

magnitude of emitted heat power which decreases with time. For this reason,

in the choice of an isotope for a generator for one purpose or another,

besides taking into account other factors it is necessary to choose a heat

power or the isotope fuel taking into account the magnitude of the useable

heat power required at the conclusion of the term of service of the given

-8-

device. Sometimes the isotope source is designed around the average value

of its thermal power for the required operational lifetime of the generator.

The basIc characteristics of radioisotopes suitable far application

as generator heat sources are given in table 1. The data on the specific

heat capacity of radioisotope fuel is taken from the literature [5, 16, 17,

29, 31, 34]. Some divergence in this data is explained by the difference in

the specific weights of the radioisotope fuels which were used.

Table 1

Ta6.iiua I

Lia u pac- f1ep1n• ninr$- I TCl.1l 6 , -tO(Z€lC,113071f PA~~v ~ z.i CMra..i. e IitCbTum* I 'wo

1. 24. 3.e4m .. 1t3)7'::,. 6.Po

07 Po "• 0.38 141.00 14;,O

Crill- Cm.O 3 a 0.15 99,5.- 120 1120,1OCI'" CI(J. :-' I.6 .2 iC113 --0". 0,-,- 1.96 -- 2.3,0 1 25.60)1;:13 P1C • 86.-*0 0.55 - 0.56 0,56

111CPm1O4, j•--'j 2.60 0.16 -- 0.'., 0.31CI -- 1? 33.00 0,2.19 - 0.33 0.42

S1i" SrTiOSrO I$ - - 27.7 - 28.0 0.113-0.92 0.9500)" CO 0--s' 5.30 0..-0 17.40RaU - T' 1.00 29,80 33.10

C111", C-..O-- c 17.60 2.30 2,80Aulia:?8Au - 1.00 29.50 -

Cr -- -- y 26.60 0.0'72TI"° TinO 3 0,35 1.03 15.R)OTiTI. 4.00 0.12 0.76TT:O, 1.90 111.00 170.* COUA• U0 2 u -- v 74.00 3.30 4.1Am74 Am 458.00 0,10 0,11

. uIsotope

2. Fuel

3. Type of decay

4. Half-life, years5. Heat power of the fuel, watts/grams

6. Heat power of the pure isotope, watts/grams

9 -

The physical and chemical properties of the compounds which contain a

radioactive isotope and are used in the form of a radioisotope fuel should

meet a series of specific requirements. The fuel should be easy to prepare,

should not react with the material of the fuel capsule, should be heat-resistant

and have a high fusion temperature. The isotope concentration in the fuel

should assure the required heat flow densities [20]. Once a fuel is obtainied

which meets these basic requirements, then various inert compounds or metallic

additives are added to it, which has an influence on the specific weight of

the fuel. This explains the divergence in data on the specific fuel power

or radioisotope fuels published in Soviet and foreign litcrature.

At the present time, a rather large ,umber of generators having a radio-

isotope heat source have been created, which has a number of advantages in

comparison with other heat sources both under space conditions and in ground

and sea installations having powers on the order of tens and hundreds of watts.

However, their application is limited by biological harmfulness. The necessity

of biological shielding leads to a substantial increase in the cost and

difficulty of generator construction.

Nuclear sources of heat energy are utilized in the development of high-

power generators. They assure extended self-contained operation of the thermo- I

electric device, and greater heat flow densities at high temperatures.

Two basic variants in the con3truction of nuclear reactors exist.

which are distinguished according to the method of heat delivery to the hot

junction of the generator: t hose having an intermediate heat carrier and those I

with indirect heat supply from heat-emitting elements of the reactor or its

internal jacket. The basic characteristics of some nuclear reactors, designed

-10 -

At"'w

-r- _.) 0)4)4

00 0 C)S. 04J 4

I- $ ) Oto r- 5 c00 CA ~lO C go~

Olt IV

Cl)S l

C4I I~' r- N

4.) 4.)

0 v

to S -. to3: CJ. CL5 04-) 0

EU ~ ~ 0 Cr-

CV.' v. 3 ap ci) 3Li CM.4)

I m

+ 55- + I+ + +

uS.. L. * S.. -?-. a.

0 f* r4 *

5- th

S- 0)0 0) Vl) o41 > a " I Ml co

E 4.)J-

S0 a CD i

0- 00 In 0ý 0CD

4.)cc ( ~n (n (n)

Ul) cn U) Vn(.(n

0L. EUoE>43 43

47 4-) 4.)

0 Cc

( n au

5-u CL CL cl. 4J 4J0$- - .

EU 00 Eq

for the '-eating of the hot junctions of generators are given in Table 2.

By means of nuclear reactors in which the heat is transferred from the

active region to the hot junctions of the generator by a heat carrier, it is

possible to provide fo: isothermal heat delivery over the entire surface of

the hot junctions, in particular where the substance used as a heat carrier

changes its aggregate state in the given power cycle. Additionally, the

intermediate heat carrier provides for partial radiation protection of the

semiconductor substance. A nuclear heat source with an intermediate heat

carrier makes possible independent construction and de-bugging of the gen-

erator and nuclear reactor. However, heat carriers in use at the present time

do not permit complete utilization of the temperature possibilities of nuclear

reactors and thermoelectric semicunductor materials.

In nuclear heat sources without an intermediate heat carrier, the thermo-

couples can be placed directly on the surface of the reflector, as was done

in the Soviet nuclear thermoelectric plant "Romashka" [17] (Fig. 1). Heat

emitting elements in the form of plates of uranium dicarbide enriched to 90%

with U-235 are located in the cylindrical graphite body of the reactor. The

active region is surrounded by a beryllium reflector, which makes it possible

to obtain a temperature of 12700 K at the surface of the beryllium reflector.

In this case, the temperature of the hot junctions of the thermucouples clamped

against the surface of the beryllium reflector was 12230 K. It is obvious

from the example of the "Romashka" plant just what importance is attached to

the refinement of the system of contact heat exchange. With a further re-

fined method of heat transfer between the contacting solid surfaces, it

would be possible to achieve much smaller temperature differences between

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Iithe heating surface and the hot junctions, which would permit a morn efficient

utilization of tie thermoelectric materials, whose maximum efficiency is

achieved at maximum operating tciiperatures.

,*q.

S-. I,1 .9 -..' -/ -'

• . *:,. g I .,C. " '

Figure 1. The nuclear reactor of the "Romashka" thermoelectric plant.

The SNAP-10 [29] thermelectric plant is of a similar construction and

is distinguished from the "Romashka" plant by the lower temperature of the hotjunctions which is 8110 K.

In plants of similar design, the plane surfaces of the nuclear reactor

are not covered with thermocouples, and require reliable insulation to avoid

beat losses, which are rather large.

Compactness and relative simplicity characterize those nuclear thermo-electric plants in which the thermocouples are superimposed on the heat-emitting

-13-Jt

MM

elements of the reactor. Any type of thermoelectric heat-emitting elements

can be employed in the reactor with the condition that the heat carrier

does not possess the property of electrical conductivity.

A series of structural variants of heat-emitting elements has been

worked out, where these are co-located with thermocouples, however they all

are modifications of a basic variant (Fig. 2). It can be seen from the

2I

5A

-6

k

• /-- 7

Figure 2. Thermocouples superimposed on heat-emitting elements:

1. Current output conductors; 5 Fuel jacket;2. Electrical insulators; 6. Fuel;3. Hot thermocouple junctions; 7. Thermocouples;4. Elek-trical insulation; 8. Cold junctions.

drawing that the thermocouples are arranged on the surface of the capsule

with a separating medium. The heat-emitting elements in such a design can

1

_o• - 14 -

-- -

-7*? - --- -- 7 - -ý 7-7 7-7 7

* be of any shape (the most widespread elements are in 'the shape of rods or

* plates).

When radioisotope and nuclear heat sources are used, the semiconductor

thermoelectric materials are subject to the effect of various forms or ad-

iation when operating, which can cause chang es in their thermoelectric prop-

erties. The gamma radiation from radioactive isotopes and nuclear reactors,

as well as neutron radiation from reactors, exerts the primary influence on

the properties of the materials. Other types of radiation accompanying a

fission reaction have little penetrating ability and are usually absorbed by

the structural elements and exert no influence on the characteristics of

the material. The questions which are connected with the influence of rad-

iation on the properties of materials are at the present time still in-

sufficiently studied. However, according to data in the literature, there

exists a largo number of semiconductor thermoelectric materials w', ch are

capable of operating satisfactorily under conditions of radioisotope and

nuclear reactor heating of the hot junctions of a generator.

The surrounding medium is usually employed as a cold source in the heat

circuits of thermoelectric devices. Depending on the purpose of the thermo-

electric device, water, air or outer space can be considered a surrounding

medium. The heat from the cold junctions of the generator or from the hot

junctions of the refrigerator can be removed to the cold source either

directly or by means of an intermediate heat carrier. The cold source has a

substantial influence on the structural and power characteristics of a thermo-

electric device, since the temperature level and the working medium determine

the rate at which heat is removed from the junctions, which in turn

1 -

~I

determines the structure and dimensions of the heat dissipation system.

2. Heat Delivery and Dissipation Systems

These systems play a significant part in the construction and operation

of thermoelectric devices and plants. "he choice in the method of delivering

heat to the hot junctions of generators and the cold junctions of refrig-

erators is determid in many cases by the weight and dimension parameters

of the devices, and their power efficiency. In the development of one type

or another of thermoelectric devices, all the basic forms ol heat transfer

are usually employed -- heat conductivity, natural or forced convection and

radiation -- depending on the purpose of the devices and the specifics of

the operational conditions. Sometimes combined systems of heat transfer are

employed, for example, the transfer of heat simultaneously by convection and

radiation.

The process of transferring the heat by heat conduction occurs when the

hot junctions of the generator which are directly clamped against the surface

conducting the heat away are heated and when heat is conducted from its cold

junctions to the surfaces in contact with them which absorb the heat. The

converse is true in refrigetating devices. The heat conductivity of the

materials j* the thermocouple branches in these cases is of great significance

in the structural design work on thermoelectric devices.

The direct transfer of heat from the source to the junctions of the

thermoelectric device makes it necessary to create a heat junction consist-

ing of several ldyers of materials of various thermal conductivity which

are air-tight, electrically insulating, electrically connecting, etc. For

-16-

this reason, the calculation of heat transfer is made based on the relation-

ships obtained for multilayered walls [28]. .

Nuclear theyrnoelectric systems of the "Romashka" and SNAP-1O type can

serve as exampljs where the proJcess of heat conductivity is utilized for con-

ducting heat •'on. the source to the hot jur~c.ions. In these systems, the

thermocoupl are arranged directly on the external jacket of the nuclear

reactor. H.ct is also supplied in a similar manner to thl. hot junctions in

radlois•t generators (Fig. 3).

siii

Psic. 3..

"TOp C . o TIIIi II ",m

Figure 3. A radioisotope generator where heat is delivered to the hot

junctions by thermal conductivity

In spite of the relative simplicity in laying out the heat transfer

process using thermal conductivity, this method has a number of substantial

drawbacks. FGr the contact between the heat-transmitting and the heat-

absorbing surfaces, success is not always met in assuring the heat-flow

densities necessary for normal operation of the device at a fixed temperature

of the heat-absorbing surface. Additionally, it is not always possible to

provide for a convenient structural connection of the generator with the heat

-17-

4 '\ .

source. Such a connection can be the reason for additional heat losses.

Convective systems for heat supply and removal in thermoelectric

devices employing gas, liquid or liquid metallic heat carriers are more

efficient. Convective heat delivery systems permit doing away with the

rigid structural connection between the generator and the heat source. For

the case of nuclear reactor heating, the convective heat removal system

maintains a lower 'emperature for the heat-emitting elements of the reactor

at the same temperature of the hot junctions of the generator and real-

izing in this case the extraction of large heat flow densities from the

acive region of the reactor. The rate of heat removal for convective heat-

ing or cooling is determined by the speed at which the medium moves, its

thermal physical properties and the shape and size of the heat emitting (or

heat absorbing) surface.

Where heat is delivered or removed from the junctions of thermo-

electric devices under conditions of natural (free) convection of the

surrounding medium, the value of the coefficients are very low.

For the calculation of the heat output coefficients a for plane

walls and pipes, the following equations can be recommended [16]:

I- , I .I <I- (GrPr)<3 lO1,Nu.- \. i G:lPrj . '.t, 5- 10 < (GrPr)> 2.10,o (1)Na 1.!3 (irr' ::.u 2. !0) <(GrPr)>2. 10',

where Nu - d g63lAt Pr c , is the volumetric

expansion coefficient, v is kiru.matic viscosity, I is the typical dimension,

At is the thermal head, x is the coefficient of thermal conductivity, cp is

the heat capacity, a is the heat transfer coefficient, and v is the dynamic

-18-

viscosity coefficient. In this case.ithe value of c 3 - 6 watts/m2 . degrees.

Where natural convection is used to increase the heat removal (heat

delivery), the junctions are equipped with fins for the purpose of increasing

the heat dissipating (heat absorbing) surface. In this case, the heat

transfer coefficient from the finned surface to the surrounding medium

depends on the shape, size and relative arrangement of the fins.

Natural cooling of the finned surfaces of junctions is primarily em-

ployed in those cases where questions of power efficiency make the consider-

ations of the weight and size characteristics of thermoelectric devices of

secondary importance.

A fin cooling system significantly increases the weight and size of

a thermoelectric device and complicates its fabrication. However, underaA

natural convection conditions it has little influence in increasing the

power efficiency of the device. For this reason, when working with gaseous

media blowers are often employed to increase the rate of heat transfer by

creating a forced flow of gas along the vanes. In many cases, the expend-

itures of a part of the useful power developed by the generator to drive a

blower is economically justified. For example, in generators for the cathodic

protection of gas piping where an additional expenditure of gas which isA

burned does not play a substantial part, a blower installation which blows

across the cold junctions, by increasing the rate of heat transfer makes it

possible to obtain a significantly greater drop in temperatures at the

junctions. This means it is also possible to obtain a greater useful power

per unit volume of the thermoelectric material.

The conoations of heat transfer where the vaned surfaces of different

configurations having ribs of various shapes are blower ventilated using

-19-

gas flows have been sufficiently well studied for their application in

various thermal devices and installations for the operational conditions

found there. However, all of this data is not generalized and there are no

sufficiently clear-cut recomiendations for computing the heat transfer co-

efficients from finned surfaces of cold and hot junctions of thermoelectricdevices.

At SKB [unknown institute - translator's note] of semidonductor

instruments, investigations into the heat transfer from the radiators of

thermoelectric devices have been carried out. For radiators with a slotted

gap, the data which was obtained on heat exchange is described by the

equation [8]:

Nu 155 Pe #"c,(2)

where Pe = vdcpy

In this case gaps having a width of from 0.5 to 1.2 mm for hydraulic

diameters of d = 1.6 - 2.2 mm were investigated. From the point of view of

optimal conditions for heat removal and aerodynamic resistance, the best

gaps had a width of 1 - 1.2 mm. Such systems assured heat removal with a

drop in temperatures of 2 - 4' K for heat flows at the junctions of the

thermal batteries of 2 - 2.5 vatts/cm2.

Sometimes it is more expedient to cool the fin junctions with water.

A comparison of the effectiveness of air and water heat removal from the

hot junctions of a thermcelectric conditioner [26] showed that the application

of water cooling can substantially increase the cold productivity of the

conditioner and its cooling coefficient with a significant reduction in

the height and ý,•uber of fins. Thermoelectric devices using water cooling

-20 -

of the junctions are more expedien. when employed on boats, sea navigation

buoys, in deep sea apparatus, etc.

The application of water cooling in the majority of cases makes it

possible in general to eliminate the vanes on the cold junctions of generators

or the hot junctions of refrigerators, which significantly simplifies the

techaulogy of battery fabrication. However, difficulties arise in this case

which are connected with salt encrustations, the presence of mechanical

impurities in the water, etc. The coefficients of heat exchange in such

cooling systems are computed in accordance with the well-known empirical

equations [18). Specifically for turbulent flow of liquids and gases in

channels:

Nu = 0.023 Re°'8 Pro. 4 , (3)

where Re - Ud , is the channel diameter, and U is the velocity of

coolant flow.

To improve the conditions for heat removal from cold junctions of the

generator, a method of absorbing the heat in an evaporating liquid has like-

wise been proposed where the liquid is subsequently delivered to the surround-

ing medit-m through a condenser with a developed heat dissipating surface [31).

Freon - 113 with an evaporation temperature of 3200 K has been used as a 3

liquid cooling agent. The design did not require pumps for pumping the cool- 1

ant back, since the cond.nsate was returned to the cold junction from the

condenser by the force of gravity.

Heat delivery systems with liquid metal heat carriers are attracting

attention in connection with the utilization of nuclear reactors as a heat

source for generators. Such heat carriers, in comparison with gaseous ones,

3

offer the possibility of significantly reducing power losses during pump-

through, improving the heat exchange process and reducing the pressure in

the nuclear reactor circuit. However, at the present time the possible temp-

eratures for semiconductor thermoelectric materials and nuclear reactors

exceeds those possible for liojid metallir heat carriers whose maximum

working temperature does not e;xceed 1100 - 12000 K.

The heat dissipation coefficients for the case of liquid metal flow

can be computed from the following relationships [7]:

for turbulent flow in circular pipes

Nu = 5 + 0.0021 Pe,(4)

Nu = 5 + 0.0025 PeC. 8;

for longitudinal flow around the rod bundles

Nu =6 + 0.006 Pe; (5)

for conditions of free convection

Nu -- 0,67 1 0)< Gr < 101,

P G=O r ( r, for (6)Nit-=0, 16 1 + nph Gr <lOs.

It is recommended that the determining dimension in these relationships

be taken as: the altitude for vertical walls, the diameter for pipes. The

relationships given here have received experimental confirmation not only for

the case of molten metals, but also for oil, water and air [7].

Quite effective in many cases are systems of heat supply and removalfV

within the thermocouples. In this case, the thermocouple branches should

be made permeable. The permeability can be created from one junction to

another by the most diverse methods. This method can even use finelyA

-22-

porous thermocouples fabricated using the methods of powder metallurgy, and

made up of individual pipes or rods of a sufficiently small diameter which

are sintered together in erder to improve electrical contact. The themo-

couples can also be perforated by electric arc, electrochemical or laser

drilling of small..diameter holes as well as by special stamping methods.

In designing such systems it is.,necessary to'know the value of the heat

dissipation coefficients both within the thermocouples between the semi-

conductor material and the heat carrier (coolant) blown through it, and at

both surfaces, the hot ond the cold.

Heat exchange inside porous capillary bodies is characterized by a high

rate due to the very developed heat exchange surface. In view of the very

small flow cross-section of the channels through which thE heat-dissipating or

tVe heat-absorbing substance blows, it does not obey the laws of heat exchange

for flow in pipes and channels.

In finely porous thermocouples fabricated using the methods •f powder

metallurgy, the internal heat exchange surface is for all practical purposes

undefined, since there are observed non-penetrating and uneven pores,

pinching of the pores in the material, etc. Volumetric heat transfer co-

efficients cx*, watts/cm3 . deg., are usually employed in such systems.

The usual geometric magnitudes cannot be used a defining dimension in the

heat-exchange equation because the geometric characteristics of the cap-

illarios cannot be reproduced in the stamping process. A magnitude charact*r-

izing the iiydraulic properties of the given sample is usually employed inthese cases.

Many works have been devoted to the investigation of heat exchange

-23-

r,'Z

within finely porous bodies which are flushed with various substances. How-

ever, no general relationship for computing the heat transfer coefficient

has been found up to now since its magnitude is determined by a large number

of factors which are difficult to assess - the properties of the material,

the stamping technology, the size of the initial powder, blow-through velocity

of the substance, etc.

The heat exchange surface within a thermocouple can be determined

precisely where permeable tC2rmocouples are fabricated by stacking rcds

together or drilling small-diameter openings. The heat transfer coefficient

a, watts/cm2 . deg., is used in the calculations for perforated thermocouples.

The heat exchange per unit volume within a material having a large number of

capillaries has been insufficiently investigated. At the present time there

are no reliable formulas for the engineering calculations of perforated

systems.

The temperature fields within permeable walls which are flushed by a

substance, will be considered in more detail in the following.

Heat exchange at the external surfaces of permeable thermocouples is

complicated by the fact that the substance is either drawn off or injected

through the capillaries. For example, when a drop in temperatures is

created at the junctions of the generator by means of flushing with a coolant

directed from the cold junctions to the hot ones, the heat exchange cond-

itlons at the hot and cold side of the generator will be entirely different.

The coolant which exits the capillaries on the hot side, creates a gaseous

layer between the hot junctions and the heating flow which significantly

increases the difficulty of heat transfer from the heating flow. The

-24-

'*U -f\24 - - - -

S" ÷~ ¾ ° , ,, " - i -

greater the output of the substance which is blown through, the thicker

this layer is, which has a temperature many times lower than the temperature

of the heating flow, inich means there is also a smaller heat transfer co-

efficient a . The nieat transfer coefficient a, from the permeable wall to

the external flow from the outlet side of the purging substance can be

computed from the formula

S( ! 1: (7)all. ,

which has been experimentally confirmed for a broad range of parameter

changes [19]; where b = 0.35 when 0.2 less than M2 less than 1, and

b = 0.7 when 1 less than M2 less than 8; aH is the heat transfer co-

efficient at the nonpermeable wall; M2 and M, are respectively the weights

of the primary flow and the substance being blown through; pv is the

specific consumption of the substance being blown through.

On the cold side of the generator where the coolant enters the capillaries,

the rate of heat transfer increases vie to a thinning of the viscosity of

the layer against the well.

Two variants of the thermal conditions can be considered for the side

where the substance enters the permeable wall. For the case where the sub-

stance exits through the surface within the permeable wall, it can be

assumed that heat losses into the surrounding medium from the cold side of

the wall are absent. The heat leaving the surface of the wall, returns

within the wall with the substance blown back in. In this case there is no

point in talking about a coefficient of heat transfer e as a magnitude

-25 -

characterizing the quantity of heat removed from the surface,

However, if a portion of the medium flow blows through a permeable wall,

while another portion flushes its surface externally, then there is an

irreversible neat loss from the cold side of the wall. It is just this

portion of the heat flow which is of the greatest interest and importance

in considering the thermal equilibria of thermoelectric devices with permeable

thermocouples. When carrying out heat calculations for such devices, it is

always essential to know the quantity of heat which is irreversibly removed

beyond their limits into the surrounding medium. The heat transfer co-

efficient a from the permeable wall to the coolant flow washing it, which

characterizes the irreversible heat loss from the given wall section, can

be determined from the following relationships [14]:

6 -3174(Re 1 -1.24 1 03.34Nu d 68• lOe3(R e) (eqv eqv

for 1 2eqv

(8)e1.74~ 1 •-I.24

Nu 0.017 Ren •(Aein eqv

for d > 2deqv

where 1 is the channel length. Taken as a defining dimension in these

relationships is the equivalent channel diameter, deqv, formed by the

I tpermeable thermocouples and the impermeable walls of ýhe structure;

Rein = iUinde1? is Reynold's number based on the flow velocity across

ini

- 26 -

based on the blow through velocity of the cooling substance through the

thermocouples; n - Pp is the ratio of the portion of the perimeterP

Ppr taken up by the permeable wails to the total perimeter of the channel.

This correction takes into account the fact that in the structural formul-

ation of the thermoelectric device, the coolant (cooling substance, heat

carrier) will be moving in the channel, and one or a few walls of the

channel will appear as permeable thermocouples. The relationships given

above were obtained experimentally as a result of studying the heat transfer

from finely porous walls when air was sucked out through them [14].

Systems using radiative heat dissipation are employed in the operation

of thermoelectric devices in outer space. Such devices should have a

cooler-radiator for removing heat from the junctions. In this case, heat

is delivered to the radiating surfaces from the junctions either by means

of thermal conductivity or an intermediate heat carrier. The quantity of

heat dissipated by radiation into outer space can be determined from the

Stefan - Boltzman equation:

Q = FcaT4 (9)

where e is the level of characteristic black body heat radiation, and

a = 5.68 * lO watts/mr2 deg4 is a constant.

The dependence of the area F of a heat exchange radiator on the

temperature T of its surface for a fixed level of heat dissipation Q can

be seen from this equation.

A ground service variant of the thermoelectric converter of the

"Romashka" space power plant can serve as an example of such a system.

In this case, heat dissipation was effected by radiation from a finned sur-

face of the cold junctions into a medium which simulated outer space

- 27 -

-N -- )

conditions (Fig. 4).

N -'---X* ... xt ..N I. ,/

lid

_I~,E I.'

Piwc. 4. Tep~oAichr lfl'cc¢•lli'• Ixpeo6pa3o3aTCJ.1b eCpIopea.•Top~lo1I

Figure 4. The thermoelectric converter of the "Romashka" nc.lear reactor

system.

3. Power Sources

If one of the basic elements for generators is the source of thermal

energy, then the power source has considerable influence on the operation of

thermoelectric cooling devices, conditioners, thermostats and heat pumps.

The choice of this source plays a substantial part since a high level low-

voltage direct current is required for the operation of thermoelectric devices.

Storage batteries, rectifiers and current converters, and DC generators which

match the parameters of the given device are usually considered as power sources.

The powering of thermoelectric devices for everyday service and fixed

-28 -

J'

industrial devices where electrical power is available is accomplished

from the mains in the majority of cases using rectifiers. However rectifiers

produce direct current with a certain percent of pulsating DC. The presence

of an alternating component in the rectified current can be quite significant

for certain rectifier device circuits. Current pulsation leads to sig-

nificant degradation in the power characteristics of conditioners or heat

pumps, and batteries operating in refrigerator modes. Therefore to preclude

this pulsation, filters of various types are used, the most widespread being

semiconductor diodes - germanium, silicon, selenium and copper oxide.

However, the use of filters for smoothing the pulsations is sometimes

made difficult since the semiconductor thermobatteries require large currents

reaching hundreds of amperes. At the present time, high current germanium

diodes for currents of 1000 amps and greater which operate at a sufficiently

high efficiency, are being industrially produced.

Investigations which were carried out in the semiconductor laboratory

of the Odessa technological institute of the food stuff and refrigeration

industry, have showi: that the current Dulsations flowing through the thermo-

batteries significantly influence their power characteristics. The reduction

in cooling productivity and the cooling coefficient of plants in comparison

with the computed values (for computations based on DC without pulsations)

can amount to 20 - 50% and more depending on the operational temperature

level of the thermobatteries, for the case of the presently most widespread

practice of using single phase full-wave rectification [20).

The power parameters of devices operating with large temperature diff-

erences at the junctions of the thermocouples are degraded particularly

-29 -

severely. These circumstances force us to strive to maximally smooth the

pulsations in current feeding thermoelectric devices. If it is impossible

for any reason to eliminate or reduce the current pulsations, then theactual design calculations should be made with formulas which take into

account their influence on the operation of the device.

Storage batteries are used to power thermoelectric devices which operate

where there is no electrical power available from the mains. The necessity

for using storage batteries arises primarily in the operation of non-stationery

devices. The operation of thermoelectric devices directly from a battery

is limited in time by its capacity. Because of the fact that such devices

use large currents at low voltages, the battery is discharged rather quickly.

For this reason, to increase the operational life of the thermoelectric

device which uses a battery, current converters are often employed which

converl "'e relatively high-voltage low-current battery output into a high-

current low-voltage supply. The presence of a converter naturally leads to

additional losses, and the efficiency of the supply circuit is significantly

reduced.

Thermoelectric generators can often be successfully employed as a power

source for thermoelectric cooling devices, heaters and conditioners. The

generator design can assure obtaining the DC parameters at the output

necessary for powering the refrigerator or heater.

A

-30 -I

Chapter II

The Classification of Heat Circuits of Thermoelectric Devices

The common packaging of the basic components considered in Chapter I

makesit possible to create various circuits for thermoelectric devices. The

creation of an effective thermoelectric plant is impossible without a detailed

analysis of the mutual interaction of elements of heat circuits which are

rigidly intercoonected during operation.

The heat circuits of thermoelectric devices are usually classified

from the viewpoint of the difference in the methods of delivering and

removing heat at the junction surfaces of the thermocouples. It is expedient

to consider generator circuits and base their comparison on the heat source

as one of the basic components of the device. As far as the circuits of

thermoelectric cooling devices, conditioners and heat pumps are concerned,

distinguishing between them on the basis of different systems of heat supply

and removal is justified.

1. Generator Circuits

The circuits of generators where the hot junctions are heated by comb-

ustion products are shown in Figure 5. Heat is delivered to the hot junctions

by convection from a gaseous flow of combustion products or an organic fuel.

These circuits are distinguished by the methods used to create temperature

drops at the junctions and the dissipation of heat from the cold junctions

of the generator. j

Devices which are made as shown in the diagram of Figure 5 a, in 7

-31-

Si -

S" which the heat is dissipated by free convection from a finned surface on

the cold junctions, are usually employed in difficult access localities where

it is impossible to constantly monitor their operation. In particular, they

can be utilized for cathodic protection of gas and oil pipe lines, located

at points distant from population centers. Under these conditf'ns, the power

efficiency of the power source does not play a substantial part, since there

is very cheap fuel available for combustion in the burner device of the gen-

erator, while the dominant factor becomes the reliability for extended oper-

ation of the device without maintenance.

"ab bc

a F' I; "'"'

Sd f• '-e

!. 3. C.-% ift' PlIao: ;3i C O| oi t OO lleb pI i ;oa'OP N . e i;: ,rC s! C'C

:•-I:ll5l, I

Figure 5. Diagrams of generators where the hot junctions are heated by

combustion products.

A generator fabricated in such a fashion will have a very low efficiency.

In the general case, the efficiency of any generator where the hot junctions

are heated by combustion products, is determined from the following expression:

= N.. n - BQH ,

p

-32 -

hPi

• where N is the useable electrical power developed by the generator; B is

•.. the fuel consumption; QH is the heat generating capacity of the burnedful

i It is well-known [6], that the useful electric power taken from the

•.generator terminals, depends on teproperties of the thermoelectric materials

Semployed, z and x, the battery dimensions, 6 and F, the temperature drop

•. across the junctions AT and the ratio of load resistance to internal resistance

S~m, i.e. :

• ,A - ' T-F lwnl.

S~It is apparent from this, that for a given material the determining factorSis the temperature drop across the junctions, for which the developed elect-

S~rical power varies as the square. The creation of the maximum possible

temperature drops across the battery junctions is conditioned in the usual

case by two such factors: the maximum achievable working temperature of the

hot junctions which is limited by the properties of the semiconductor thermo-

electric material which is used, and the rate of heat dissipation from the ,

cold junctions. In this case, it is hypothesized that a heat flow density

necessary to maintain to maximum temperature of the hot junctions for any

cooling rate of the cold junctions can be assured from the hot side of the

thermobattery. The required heat flow density in the burning region can be

Sachieved by changing the fuel expenditure and the excess oxidate ratio, as

well as by creating optimum aerodynamic conditions for a high heat-exchange

rate. Naturally- when cooling the cold junctions by free convection into

the surrounding medium, it is impossible to assure %,he removal of largegequantities of heat because of the very low heat transfer coefficients under

athese conditions. This means that it is impossible to achieve any kind of

S- ~33 -

* large temperature drops across the junctions. For this reason, in designs

based on the drawing shown in Fig. 5 a, the useful power derived per unit

surface of the thermobattery is usually very small. An external view of one of

the first Soviet generators, the TGG-l0, which was fabricated along the lines of

the diagram shown in Fig. 5 a, is shown in Fig. 6. This generator developed

a useful power of 10 - 12 watts at a current level of I amp r4].

I .r .. Figure 6. The TGG-10 generator.

J. Y

The efficiency of devices operating on combustion products are still

rather low at the present time, primarily for two reasons. In the first place,

all of the heat derived fi-om the cold junctions is dissipated into the

surrounding medium and lost without serving any purpose, and, in the second

place a substantial amount of heat is lost with the exhaust gases. Nhile it

still might be possible to deal with the first heat loss somehow by effecting

heat regeneration (see Fig. 5 b), the matter is more complicated in the case

of heat losses with the exhaust gases.

The combustion products leave the thermoelectric device with a temp-

erature exceeding that of the hot junctions. Such a situation exists in all

of the designs produced at the present time (see Fig. 5 a and b), as well as

in the circuits shown in Fig. 5 c and d which have not yet been considered.

The heat which is lost with the exhaust gases in gererators running on organic

fuels appears to be basic for determining their low efficiency.

For the case where the branches of the thermocouples are fabricated

from high-temperature thermoelectric materials, the combustion products leaving

-34-

the device have a high temperature and can be used in any other heat utilizing

device as a working medium. In this case, the generator plays the part of a

high temperature addition to the basic cycle increasing its power efficiency. itThe overall efficiency of such a combined cycle is determined according to

the following relationship [27]:

nk + (I - no), +

where no is the efficiency of the basic cycle; n is the efficiency of the

high temperature addition (efficiericy of the generator); p is the coefficient

equal to the ratio of the heat delivered to the generator, to the heat

transferred directly to the additive cycle.

When a generator is used as a high temperature addition to a cycle which .

has an efficiency commensurate with its efficiency, the efficiency of the

combined cycle can be increased almost two times. This will be the case when

a high temperature generator is utilized jointly with a low temperature one.

The structural diagram of a generator intended for operation using

organic fuel and fabricated according to the diagram with recovery of the

heat which is removed from the cold junctions (see Fig. 5 b) is shown in

Fig. 7. This generator which was developed in the USA can be made with a

variety of useable electric power levels [16]. The design of such a generator

provides for the possibility of utilizing any liquid organic fuel. The

liquid fuel is located in a fuel tank under excess pressure. When the gen-

erator is operating, it is fed through a line into the ce'buretion chamber.

Upon the evaporation of the fuel in the carburetion chamber, air is sucked

in there from the surrounding medium through an inlet opening, and a gas-air

mixture is formed in the chamber which is then fed into the combustion chamber.

33

(-n

13 • \

12 ... .

- - 20

JL 2 -24

3-ý

8 - 22

J17-i

5-I -- 22

---- '-' i23

* Figure 7. The construction of a typical generator which operates on liqi:'d

fuel :41I. Stiffening ribs; 20. Profiled cone;2. Ejector; 21. Fuel container; ,- 3. Radial fuel channels; 22. Frame cowling;4. Liquid fuel; 23. Combustion chamber cowling;5. Axial fuel valve; 24. Igniter;i7. Carburetion chamber 26. Bottom of tlne carburetion chamber;

28. Cooling surface; 27. Annular fuel line;-9. Combustion chamber; 28. Air flow channel s o;,10. Heating surface; 29. Nozzle; cn

j . 11. Fuel pump; 30. Frame;12. Air outlet opening; 31. Fuel line;13. Flow mixer; 32. Supports; c i14. Housindgful; 33. Regulating valve;15. Exhaust 3ipe; 24. Fuel flow channel;16. Exhaust opening; 35. Ejection channels;17. Cap; 36. Air inlet opening;18. Flange; 37. Air cavity;19. Current output leads; 38. Bottom of the combustion chamber.

-36 - I

Heat is lelivered to the hot junctions of the thermocouples from the com-

bustion products using fins which are mounted on the combustion chamber

surface. The finned surface of the cold junctions is cooled by air which is

circulated by the pressure difference between the inlet and outlet openings,

which is created by the venturi action of the exhaust gas flow. A partial

recovery of the heat removed from the cold junctions of the generator is

realized by transmitting it through the cooling surface and the wall of thefuel container to the fuel.

Diagrams of generators which differ in principle from those made at the

present time in the method of creating a temperature drop at the junctions are

shown in Figures 5 c and d.

As has been noted in Chapter I, the thermocouples of such generators

should be permeable to the blow-through of a substance in a direction from

one of the junctions to another. When a device based on the diagram shown

in Figure 5 c is operated, the cooling medium blowing through the permeable

thermocouples and which in removing the heat within the thermocouples creates

a temperature drop across their height, upon exiting the surface of the hot

junctions mixes with the heating flow. On the other hand, in a device which

operates according to the diagram shown in Figure 5 d, the hot gas blowing

through the thermocouples transmits the heat within them and having created a

temperature drop across the junctions exits the surface of the cold junctions

and mixes with the cooling flow.

The primary distinction between these systems and those now being made

consists in the fact that the basic quantity of heat is supplied (removed)

not through the -irfaces of the hot (cold) junctions, but within the thermo-

-37-

* x*4 4

couples through their highly developed internal heat exchange surface.

As noted above, owing to the characteristics of heat exchange in finely

porous or capillary systems, the heat from the ventilating current is trans-

mitted to the material of the thermocouple branches (or vice versa) with an

insig~ificant difference in the temperatures of the heat-exchanging medium,

i.e. almost thermodynamically reversibly. This implies that within the thermo-

couples, the temperatures of the material and the ventilating substance will

be the same or very close to one another over their entire heglht. The

temperature profiles in the blow-through systems and their influence on the -

power characteristics of thermoelectric devices will be considered in sub-

sequent chapters.

The fabrication of permeable thermocouples from many thermoelectic

semiconductor materials will present no particular difficulties in comparison

with the fabrication of monolithic thermocouples from the same materials.

The technology of stamping finely porous permeable samples is well worked

out for a whole series of both metallic and metallic-ceramic materials and

requires only finishing work for many semiconductor thermoelectric alloys. It

is apparent from operational experience that the creation of permeable thermo-

couple branches is a completely resolvable problem. The greatest complexity

Ni the creation of finely porous batteries is offered by the solution of the .4

problem of series parallel connection of the branches of the thermocoupleswhile preserving the permeability of the interconnected surfaces.

In considering the expediency of using permeable thermocouples from the

point of view that there is an inadequately developed technology for their

* fabrication at the present time, it should be noted that permeatility can

be created using not only the methods of powder metallurgy but also other

38 -

methods. For example, permeable thermocouples can be obtained by means of

electrochemical or electric arc drilling of sufficiently small diameter

openings in monolithic thermocouples which are manufactured in accordance

wit~h a well-known and well-developed technology. The electrode with which

the openings are made can be fabricated in the form of a comb which permits

the simultaneous piercing of a set number of openings. Such a method of

creating permeability is entirely justified when working with comparatively

soft thermoelectric materials. Thermoelectric modules consisting ot five

p - n pairs, whose branches are made from thermoelectric semiconductor

materials on a Bi, Te and Se base are shown in Fig. 8. In each square f

.. . . . . . . . .... . . . . .. .... -F 7

Figure 8. Thermoelectric modules with permeable thermocouples. I4i

centimeter of the material of the branches iin these modules, there are fifteen

openings with a diameter of 0.45 - 0.55 mm. The divergence in hole

diameters is explained by the fact that the tungsten electrodes of the comb

were not ideally even and parallel with respect to each other.

- 39 -

For hard, difficultly fuseable materials (for example silicide),electric arc processing requires a loc of time, and for this reason this

method is little used for the fabrication of a large number of holes. There-

fore, thermocouples of refractory thermoelectric materials can be manufacftured

using the method of dross casting or press forming a powder. At the present

time, test samples of perforated thermoelectric modules of high-temperature

materials have b 'n obtained using the manufacturing methods of press-forming

powder metallurg, Thermocouples can likewise be obtained by sintering

previously pressed small-diameter rods or pipes or by other methods.

The diagram sho'n in Figure 5 c permits complete recovery of the heat

removed from the cold junctions of the battery as does the diagram of Figure

5 b, however it has a large number of advantages in comparison with the latter.

In the operation of a generator in accordance with the second diagram,

the temperatures of the heating and cooling currents, and thus the temperatures

of the junctions, will change sharply along the length of the generator.

Additionally, for the case oi convective heat delivery to the hot junctions

and convective cooling of the cold junctions, significant parasitic temperature

drops exist both at thý. hot side of the thermobattery (between the heating

flow and the hot junc•ions), and at its cold side (between the cold junctions i

an,; 'Uh cooling flow). Fin cooling of the junctions is employed to reduce

these te;rperature differences, which makes the construction of the generator $

significa't.ly more cumplex and difficult. This hinders the possibility of

more or less completely utilizing the maximum temperature head, between the

initial temperature of the heating gas and the temperature of the cooling

substance at the inlet to the device.

-40 -4

The circuit shown in Figure 5 c makes it possible to eliminate a

* . substantial number of the defects of the circuit shown in Figure 5 b.

In the first place, when using permeable thermocouples such operational

modes are possible that sufficiently large velocities of the blow-through

medium assure equal or aln.ost entirely equal cold junction temperatures and

coolant temperatures. Consequently, it is possible to almost completely

exclude a parasitic drop in temperature at the cold side, which maintains

the temperature of the cold junctions of the battery constant. over its entire

length and close to the temperature of the cold source. For example, this is

possible by sectionalizing the delivery of th2 cooling medium, when the length

of the sections is chosen in such a fashion that the coolant does not have

time to warm up in the cooling canal by the time it reaches the inlet to the

capillaries at the side of the cold junctions.

Secondly, either an oxidizer or a fuel can be employed in such a gen-

erator as a cooling medium which is blown through the permeable thermocouples.

The oxidizer (fuel) which is fed in along the length of the generator also

makes it possible to maintain the temperature of the hot junctions nearly

constant over the length of the generator, i.e., as calculations show, at a

quite significant distance from the comDustion chamber (from the first thermo-

couples). This is achieved by gradually burning up the fuel in the oxidizer

injected through the thermocouples, or vice versa, by burning the fuel which

is blown through the thermocouples, in the current of the oxidizer which is

fed in surplus over the first thermocouples.

Despite the difficult conditions of heat supply to the hot junctions

(see Chapter I), the circuit considered here yields the maximum temperature

-41-

I.

IA

drop at the junctions, most completely utilizing the temperature head

established between the hot and cold heat sources.

In such a fashion, under ideal conditions the circuit considered here

can assure constant temperatures for the heating and cooling currents over

the entire length of the battery while preserving the maximum temperature

drops at the junctions. In this case, the cooling medium consumption necessary

for creating the same temperature drops at the junctions of the circuit of

Figure 5 c is incommensurably smaller than is the case for the operation of

the circuit shown in Figure 5 b, even when finned cooling of the cold junctions

of the batteries is present in the latter circuit.

A comparison of the power parameters of devices based on the circuits

shown here when they are used as a high-temperature addition to some thermal

cycle (the consumption and parameters of the hot gas input flcw are given)

shows that the circuit of Figure 5 c assures a significantly greater useful

electric power, other conditions being equal. A more detailed analysis of

the operation of a generator made according to the diagram shown in Figure 5 c

will be set forth in the following chapter.

If in the circuit of Figure 5 c the temperature drop across the junction

of the battery is created by blowing roolant from the cold junctions to the

hot ones (against the heat flow), then in the circuit of Figure 5 d, the

temperature drop at the junctions is created by blowing the heat carrier in

the opposite direction. In devices which are built based on such a heat

circuit, the high temperature combusticn products blow through the permeable

thermocouples from the hot junctions to the cold ones, and in giving up their

heat within the material of the thermocouples create the conditions for

- 42 -

normal generator operation at a sufficiently high rate of heat removal from

the surface of its cold junctions. Owing to the high rate of heat exchange

on the hot side when heating gas enters the capillaries, these circuits make

it possible to have the temperature of the hot junctions approach as closely

as possible the temperature of the hot source. If the combustion produccts

flowing across the first thermocouples of the generator have the same temp-

erature, then the temperature of the hot junctions can be maintained constant

along the length of the generator where hot gas is delivered to the thermo-

couples either sectionally (as in the cooling case) or from a closed volume

perpendicular to the hot junctions. Such a circuit permits maximally util-

izing the temperature possibilities of the heat carrier. A generator based

on this circuit, is suitable for application as a device which utilizes the

heat of the exhaust gases of any heat-using device. In particular, the utili-

ization of such a device as a second-stage generator which is made based on

IIthe circuit of Figure 5 c yields a significant increase in the efficiency of

the thermal cycle of this device (see Figure 5 f) [27].

In contrast to all of the circuits considered above, the circuit in

Figure 5 d makes it possible to reduce to a minimum the loss of heat with

exhaust gases. In fact, owing to the high rate of heat exchange within the

thermocouples, real conditions can be created to assure that the heat carrier

exits the cold side of the junctions at a temperature close to the temperature

of the cold junctions. For this reason, the heat carrier will leave the

device at a temperature close to the temperature of the surrounding medium

given a sufficiently high internal cooling rate for the cold junctions.

Combined generator heat circuits are shown in Figures 5 e and f. The

-43-

circuit shown in Figure 5 e represents two generators based on the circuits

of Figure 5 b and c and co-located in o,;e independent unit. The first high-

temperature stage of such a generator makes it possible to obtain the maximum

possible temperature drop for the given conditions at the junctions by inject-

ing fuel through the permeable thermocouples and gradually burning it in an

oxidizer fed in excess to the input. The second stage o fthe device under

¶ consideration, the low temperature one, utilizes the exhaust heat from the

first stage combustion products and increases the overall efficiency of the

plant.

The circuit of Figure 5 f is most efficient in generators which run on

organic fuel. It permits the operation of both generator stages while realizing

the maximum possible temperature drop at the junction and in this case, reducesC

the heat losses from the side of the cold junctions and the losses with the -

exhaust gases to a minimum.

A more detailed analysis of the operatieni of circuits having permeable

thermocouples (of this and the others described above), as well as the proced-

ure for computing them will be set forth below.

Circuits of generators with nuclear reactor and radioisotope heating of

the hot junctions are shown in Figure 9.

The circuits depicted in Figures 9 a and b are distinguished from the

generator circuits using combustion products for heating which were considered

above (see Figures 5 a and b) only by the method of heat delivery to the hot

junctions. In this case, the hot junctions are heated by direct thermal

contact with the heat-radiating surface. In these circuits, either an external

nuclear reactor jacket or a capsule containing radioisotope fuel can be

4- 44 -

cons'dered as a heat-radiating surface. Circuits in which the utilization

of heat which is liberated during the fission reaction of radioactive sub-

stinces, is proposed for heating the hot junctions of thermocouples, have

the same drawbacks as the analogous systems using combustion products for

junction heating which were described above.

a •b

2

Ld.i I %,'- _UT, -

/ -ai i u--- -- a

-I I •l• -• -',.

, ,t,,,- I¼,

Figure 9. Generator circuits with nuclear reactor and radioisotope heating:

1. The heating surface;

2. Thermocouples;

3. System for cooling the cold junctions;

4. Heat carrier loop;

2 I 5. Heat exchanger.

45-

The circuit shown in Figure 5 b is most suitable when a device is

employed where there is cold water for creating a large temperature drop at

the junctions (for a high rate of heat removal from the cold junctions of the

thermocouples). Such a circuit has been realized in a rather large number

of generator designs for sea duty. The sea-going power system which was

based on the SNAP-10 nuclear reactor intended for service in the space program

car, serve as an example. This system provides an electrical power of around

350 watts from 100 thermocouples.

In this device, the thermocouples are situated between the external

surface of the reactor and the internal frame of the power plant. Heat dissip-

ation from the cold junctions of tha batteries is effected using thermal cond-

uctivity through the wall of the external frame into the ocean medium [33].

At the same time, a power system for space service based on the same reactor

(Figure 9 a) where heat was dissipated by radiation From finned cold junctions,

yielded a useful electrical power of only 250 watts.

The circuit of Figure 9 c is also rather widely used in the development

and fabrication of thermoelectric devices for both space and sea-going service.

The SNAP-lOA thermoelectric system (Figure 9 c) functioned in a near-earth

orbit at an altitude of 1300 km for 43 days in 1965, generating a useful power

of more than 500 watts during initial operation (up until an accident). A

schematic of the operational cycle of this plant is shown in Figure 10. Heat

from the active region of the reactor is transmitted to the hot junctions of

the thermocouples by a liquid metallic heat carrier, NaK-78. The given gen-

erator is made up of 2880 thermocouples, consisting of germanium - silicon

alloys. Heat from the cold junctions in this circuit is likewise removed by

- 46 -

an intermediate heat carrier, which is cooled in the heat exchange radiator.

The surface of the heat exchange radiator was 5.8 m2 at an average temp-

erature of 5970 K [31, 34]. Thermoelectric converters for sea-going service

havii.l a useful electric power of 500 - 2000 watts were developed on the

basis of this same nuclear system. Eutectic sodium - potassium was used

both for delivering heat from the reactor to the hot junctions of the gen-

erator and for removing heat from the cold junctions to the heat exchanger

which was cooled by sea water [33]. This system has successfully undergone a

long period of testing.

1 . :\i

67if

31(1

3.

Figure 10. Diagram of the operational cycle of the SNAP-1OA power plant.

1. Pump; 2. Reactor; 3. Thermoelectric converter. I

A substantial advantage of the circuit depicted in Figure 9 c is the

fact that the intermediate heat carrier serves as additional radiation

shielding for the thermoelectric semiconductor materials. This makes itpossible to somewhat increase the number of materials capable of operating

-47-AI $

from a nuclear heat source. However such a system makes the utilization of

high-temperature materials more difficult insofar as at the present time there

is no adequate high-temperature heat carrier which n:eets the specific require-

ments for operation with nuclear power plants.

The deep sea device of "Neptune" system having an electrical power of15 kw was designed on the basis of the circuit of Figure 9 c and is shown

in Figure 11. The most technologically developed basic components of the

SNAP-IOA, SNAP-8, and SNAP-2 systems which were intended for space service

are combined in the device [33]. The heat power of the nuclear system is

400 kw at a temperature in the active region of 9380 K. The nuclea, -

is situated in the lower part of the device. The drive motors for thr

rods are located above the reactor and separated from its framework by

shielding. The generator which consists of 12,000 elements of lead telluride

is located in the central section of the power plant. Heat to the hot junctions iof the thermocouples is supplied by liquid NaK-78 which is heated in the active

region of the reactor from 700 to 9380 K, while the heat from the cold

junctions to the radiator is carried by boiling water which is circulated by

its own natural forces. Heat is removed from the surface of the radiator

by the surrounding sea water.

Generators can be made more compact where nuclear reactors are used For

heating and the the-mocouples are situated in the active zone directly on the

heat emitting elements.

The circuits of such converters which are shown in Figure 9 d, in contrast

to the circuits of Figure 9 c make it possible to avoid excess heat losses by

* the heat carrier in the piping, which connects the nuclear reactor with the

-48-

generator. Additionally, the indicated circuits offer the possibility of

utilizing high-temperature thermoelectric materials. However, in the design

of thermoelectric devices based on this circuit, particular attention should be

given to the radiation resistance of the thermoelectric materials, insofar

as under these conditions they will be operating without radiation shielding.

1. Instrument compartment;

1 2. Heat shielding;

3. Thermoelectric generator;

-- 2 4. Water shielding;

5. Expansion compensator;

6. Pump;,. 7. Control rod drives;

- J 8. y radiation shielding;

9. Support shell;

. 10. Reactor;11. Biological shielding.

Figure 11. Thermoele>..ric device of the "Neptune" system:

-49 -

"-E J 1, 7 '~

The circuit of Figure 9 e is distinguished from the heat circuit of

Figure 9 d by the means which are used to create a temperature drop at the

generator junctions and supply heat to the hot junctions. In the circuit of

Figure 9 d, the heat carrier removes heat at the surface of the cold junctions

and exits the boundaries of the active region of the reactor at a temperature

somewhat lower than the temperature of the cold junctions. Heat is supplied

to the hot junctions of the thermocouples from the jacket of the reactor

heat-emitting elements.

In the circuit of Figure 9 e, provision is made for utilizing permeable

thermocouples in the generator construction; at the junctions of these thermo-

couples a temperature drop is created by the blow-through of the heat carrier

from the cold junctions to the hot ones. Taking the heat from within the

thermocouples, the liquid or gaseous heat carrier exits into the space between

the hot junctions and the jacket of the heat-emitting element, at a temperature

somewhat lower than (or equal to) the temperature of the hot junctions. The

heat carrier is heated up in the gap, contacting the jacketing of the heat-

emitting elements, which are at a higher temperature; the heat carrier leaves

the reactor boundary at a temperature equal to or greater than the temperature

of the hot junctions. In this case, the heat to the hot junctions is supplied

by convection from the jacket of the heat-emitting elements and by thermo-

conductivity via the liquid metallic heat carrier or by convection and rad-

iation when a gaseous heat carrier is employed.

It is apparent from a comparison of these two circuits, that in the circuit

of Figure 9 e, all other conditions being equal, the utilization of heat from

the hot source will be greater than in the circuit of Figure 9 d, since

the heat carrier is heated to a higher temperature. However, this does not

- 50 -

____ * .~ -. ~-i4 *I\

~ - *~,. -

mean that the efficiency of the device based on the circuit shown in Figure 9 e

will be notably less than a device based on the circuit depicted in Figure 9 d.

This should be considered in connection with the conditions of heat dissip-

ation into the surrounding medium from the surface of the heat exchange cooler,

which is delivered there with the heated hcat carrier and should be dissip-

ated prior to its being fed back into the nuclear reactor.

If heat from the surface from the heat exchanger is dissipated by either

natural or forced convection, then the circuit of Figure 9 e has no advantages

over the circuit of Figure 9 d, insofar as during an increase in the temp-

erature head between the surface of the heat exchanger and the cooling medium,

the quantity of heat which has to be dissipated increases. The linear relation-

ship between the quantity of heat dissipated in the heat exchanger and the

difference in temperature between the heat radiating surface and the cooling

medium (in accordance with Newton's law) Q = aF (T - t) does not permit a red-

uction in the surface of the heat exchanger or an increase in the degree of

cooling of the heat carrier.

When heat is dissipated by radiation, the quantity of heat removed from

the surface o^ the heat exchanger depends on the 4th power of its surface

temperature (see (9)). Under these conditions, the circuit shown in Figure 9 e

exhibits substantial advantages. The feed of the heat carrier into the heat

exchange radiator at a temperature exceeding the temperature of the hot junc-

tions of the generator, makes it possible to reduce its surface, or for the

same surface, cool the heat carrier to a lower temperature, which in turn

makes possible a greater temper'ature drop at the junctions of the generator.

An investigation of the parameters of refrigerator radiuators which is

-51-

* 1 '

described in the literature [24], has shown that for liquid heat carriers,

the dependence uf the surface area of the refrigerator on the quantity of

dissipated heat and the temperature of the heat carrier, Tin' at the input

to the heat exhanger and at its ou'tput, Tout, has the form:

(Tin) v•.• ~F - out •

"out ToutTin

Consequently, the circuit shown in Fig. 9 e permits an improvement in

the size and weight characteristics of the power plant for the same electrical

power by reducing the dimensions of the cooler radiator where the heat carrier

is fed into it at a higher temperacure than in the circuit of Fig. 9 d, and

conversely, for the same surface areas of the heat exchange radiator in a

device based on the circuit of Fig. 9 e, it is possible to obtain a greater

useable electric power (a greater temperature drop at the junctions) than in

the circuit of Fig. 9 d because of the more extensivw cooling of the heat

carrier. The comparison of the power efficiency of these thermal circuits

requires more detailed and concrete calculations.

.----- T< .-- :- - - - . . . . • ,. .,---. .

I, I , ' -=-'. •- " - " '

;a b •cP:.c. :2.Cx--:v 4 Ce::e-.,I-M;; Harpeam..

Figure 12. Diagrams of generators with solar heating.

The circuits of generators where the hot junctions are heated by

radiant energy from the sun are shown in Fig. 12 and are differentiated

-52-

S" according to the methods used to create temperature drops across the thermo-

couple junctions. In all of these circuits, heat is delivered to the hot

thermocouple junctions in the form of radiant solar energy. For this

purpose, in units intended for ground service using such generators, devices

for concentrating solar radiation are usually employed in view of the in-

adequate thermal density of solar radiation per unit of the earth's surface.

The heat which is removed from the surface of cold junctions of gen-

erators based on the circuits of Fig. 12 a and b is completely lost. It

cannot be recovered due to the specificity of the heat energy source. The

use of a heated cooling agent in any other heat utilizing devices is likewise

inexpedient, insofar as it is at a low temperature, lower than the temperature

of the cold junctions of the generator, which naturally has-a negative effect

on the efficiency of solar plants. However, for these devices which have

a heat energy source "free of charge", the magnitude of the efficiency does

not play such an important role as it does in generators having other heat

sources for heating the hot junctions.

A more important factor determining the practicability of obtaining

electrical energy using solar generators is their cost. The working out

of technological processes for fabricating solar thermoelectric plants is

in many respects connected with this cost reduction for devices to focus the

radiant energy of the sun, and strictly speaking the further development of

serticonductor batteries will permit their wider application in regions

having a large number of deys of sunshine.

A large number of generators with solar heating based on the circuits

of Fig. 12 a and b have been fabricated and tested at the present time.

-53 -

They are designed to obtain useful electrical powers of up to several

tens and even hundreds of watts [3].

A solar generator which uses reflectors for concentrating solar energy,

characteristically has a non-uniform distribution of thermal currents (incl-

uding temperature) at the surface of the hot junctions of the semicond-

uctor thermocouples. In this case, the thermal operational modes of the

thermocouples in the battery vary, which has a negative e., -t on its over-

all efficiency. The non-uniformity in the heating of the hot junctions in

many designs achieves rather large magnitudes, even hundreds of degrees.

However, as noted in the literature [15], for some thermoelectric materials

the heating non-uniformity can not only reduce the efficiency of generator

operation, but can also somewhat increase it due to a further increase in

operational efficiency of some thermocouples at temperatures varying from

the design average. This circumstance is completely determined by the temp-

erature depen~dence of the figure of merit, z, of the thermoelectric materials

employed. if the quantity z increases with an increase in the temperature of

the hot junctions, then the conversion efficiency grows in comparison with

the operatioi.l efficiency of the device for the case of uniform heating, due

to an increase in the temperature of the hot junctions for the average number

of thermocouples determined by the generator design. When materials are

used where the figure of merit varies inversely as the temperature, a non-

uniformity in the thermal flow on the hot junction side causes a reduction

in generator efficiency.

The effort to assure uniform temperature conditions in the battery

* thermocouples led to the creation of solar generators having thermocouples

-54-

of various heights and generators where each thermocouple was heated with

its own concentrating reflector.When the circuit of fig. 12 c is employed, it is possible to obtain

a coolant at a significantly higher temperature than in the circuit of

Fig. 12 a and b, which PrOvides for the possibility for its further effect-

ive utilization in other devices or in other stages of the generator. As

has been noted above, in designs using permeable thermocouples, the coolant

exits the surface of the hot junctions at a temperature close to the temp-

erature of the junctions. In such a fashion, a generator based on such a

circuit makes it possible to simultaneously obtain useful electrical power

using solar energy and a hot heat carrier for further utilization.

2. Circuits of Refrigerators, Conditioners and Heat Pumps

In thermoelectric heating and cooling devices, the temperature diff-

erence at the hot and cold junctions of the thermocouples is created by the

Peltier effects, which are manifested with the action of the flowing elect-

rical current. In these devices, the DC power source is a component of the

thermal circuit, analogous to the energy heat source in generators.

If the sources of heat energy define the various thermal circuits of

generators, then the circuits of thermoelectric heating and cooling devices

are expediently classified only froni the point of view of the differences in

tne systems for supplying ind removing heat.

Specific demands 'see Chapter I) are made on the DC power sources In

order to; assure normal operation of the device. In the analysis of the

circuits of coolers, heatV•rs and conditioners, the investigation of the

influence of the type and characteristics of the power sotrce on the other

55 -

circuit elements is of no interest so long as it meets all the necessary

requirements. Consequently, the circuits of these devices are to be dis-

tinguished primarily according to the methods of supplying and removing heat

from the junctions - radiatinn, convection (natural and forced) and heat

exchange within the permeable thermocouples.

Possible circuits of coolers, heater and conditioners are shown in Fig. 13.

5 C. 2d.

Figure 13. Circuits of refrigerators, heaters and conditioners.

1. Cooling

Systems for supplying and removing heat by radiation are not used in

practice in view of the low operational temperatures of the hot or cold

junctions of these devices. Heat dissipation from cold junctions by rad-

iation is achieved for practical purposes in thermoelectric refrigerators

for space vehicles.

In the existing conditioner and cooler designs, the most widespread

method of heat: delivery and removal ises a convective gaseous or liquid flow

across finned junctions. In this respect, batteries are classified

a56 -

according to the nature of heat removal in the battery: of the type air - air,

liquid - liquid, and a combined, liquid - gas. Batteries of all of these 4

types operate according to the circuit shown in Fig. 13 a. Fins of various

types are employed to increase the rate of the heat transfer process at the

hot and cold junctions of such devices.

In some cases, the heat removal from the hot junctions or the heat supply

to the cold junctions in refrigerating devices is accomplished not by means

of convection at finned surfaces, but by means of contact heat exchange with

a cooled or heat-absorbing surface. Such refrigerators are sub-classified

into the mass - mass and mass - air types.

The circuit of a thermocouple in which heat exchange at one of the

junctions Is realized using convection with the surrounding 'Mcdium, while at

the other by contact heat exchange with the mass of the body, is shown in

Fig. 13 b. 'IThe basic circuit of a refrigerator shown in Fig. 14 corrisponds to the

circuit shown in Fig. 13 a [2]. In such a refrigerator which is intended

for operation in a vehicle, heat is supplied to the cold junctions by the

natural convection of the air contained in the cool volume. Heat is dissi-

pated by the air flow washing over the hot junctions of the thermocouples.

This design makes it possible to maintain temperature drops between the

surroundings and the internal cooling volume of up to 2980 K.

A diagram of a thermal battery module, the thermoelectric PTK-l

chamber, developed at the SKB semiconductor institute of the USSR Academy

of Sciences, which is intended for the investigation of various devices

is shown in Fig. 15 [25). This module consists of two cascaded thermo-

couples and is capable of developing a cold productivity of 11 watts

-57-

where 453 watts of electrical power are consumed. Heat is delivered to the

cold junctions of the thermocouples from the cooling volume via a finned

surface, and heat is dissipated from the hot junctions to the body plate

by contact iheat exchange. To increase the rate of heat transfer in the plate,

through perforations are made through which cooling water circulates. In

this fashion, combined heat removal based on the circuits of Fig. 13 a and b

is realized in this case.

.l.',i~ l, ., ' I)~l.,"•

.J)

Figure 14. Schematic of a vehicle air conditioner:

1. Heat insulation;2. Refrigerating chamber;

3. Contact grease; 3I4. Heat conducting plate;

5. Cool air.

The circuits of permeable thermocouples in which the cooling medium

blows through cipillaries (pores) from the hot junctions to the cold ones,

giving up hea-; to the material of the thermocouple branches over their

entire height are shown in Fig. 13 c.

In permeable thermocouples, in contrast to monolithic types, heat is

removed from the cooling medium not at the surface of the cold junctions,

-58 -

but in the volume of the thermocouple. Heat can be dissipated from the

surface of the hot junctions in two ways. When the cooling medium. circulates

in a closed loop, a device based on the circuit of Fig. 15 c is practicable.

In this case, the cooling medium is fed into the thermocouples via channels

made in the connecting plates of the hot junctions, while any other substance

serves as a heat carrier for removing heat from the hot junctions.

,IL I ,, J , I[I U U .• 11 I u

- , iw. 15. Cxe, a , I6 ,I hi a :.i , [H .1:

" " boI I,'ll) K e aX,| 3]I I • ' 1''

2,>:- . -• ._- --=2". - ;

Figure 15. Schematic of the PTK-l battery chamber:

1. Copper plate;

2. Current lead to the first cascade;

3. Copper leaf;

4. Flexible copper needles;

5. Radiator;

6 Thermal junctions;

7. Branchus of the thermocouples;

8. Lead demping plate;

9. Copper connecting plate.

-59-

1k7

The operation of a permeable thermocouple using an open-ended circuit,

shown in Fig. 13 d, is likewise possible when heat from the hot junctions is

removed by the flow of a substance, some portion of which is sucked out

through the permeable theiinocouples being cooled.

The operation of permeable thermocouples cooled by medium flows will 4 .

be considered in more detail in Chapter V.

CHAPTER III

Features of Temperature Fields in Permeable Thermocouples

we will now consider in detail the principal distinctions in the del-

ivery and dissipation of heat at the junctions of monolithic and permeable

thermocoupl es.

Where permeable thermocouples are employed, the primary heat quantity is

removed from or delivered to the material of the thermocouple branches not

through the surface of the hot or cold junctions, but within the branches of

the thermocouples. As has already been noted, the branches of thermocouples

are made porous or perforated which causes them to have a highly developed

internal surface. When a heat carrier or cooler is blown through such

permeable thermocouples from one junction to another, the heat exchange

process between the flushing substance and the material of the branches

transpires at a very high rate. The enormously high rate of heat exchange

under such conditions is achieved due to the extraordinarily developed heat

exchange surface.

For finely porous pressed materials, the volumetric heat transfer

-60-

• g

coefficil.nts from the material of the wall to the gas blowing through the

capillaries reach the order of l05 watts/m3 x deg. In perforated walls

with capillaries having a diameter of up to 1 mm, the I*eat exchange coeffi-

2 .Icients to the gas blowing through them can amount -o 100 watts/mr • deg

and more. In this case, the large heat exchange area makes it possible to

transfer very large quantities cf heat from the heat emitting surface to the

heat absorbing medium, which determines the small temperature differences

between the heat absorbing and heat emitting media, at which temperature

the heat exchange takes place within the permeable thermocouples.

The temperature difference between the heat emitting surface and the

heat absorbing medium during the heat exchange process determines the

thermodynamic loss process. The smaller this difference, the greater are

the losses as a result of the irreversibility of the heat exchange process.

Consequently, in permeable thermocouples where ';: main quantity of heat is

supplied (removed) within the thermocouples at a sma~l temperature difference,

this loss from the irreversibility of the heat exchange can be minimal.

Where heat is supplied (removed) through the surface of the junctions

in monolithic thermocouples and the rate of heat exchange is not so signifi-

cant, and the heat exchange surface is immeasurably smaller, the loss due

to heat exchange irreversibility is large because of the high temperature

heads between the heat exchanging media. Mounting fins on the junctions

makes it possible to somewhat reduce such a loss. However, this is achieved

at a substantial increase in construction cost and complexity.

The presence of internal heat exchange in permeable thermocouples

introduces fundamental and important factors into their operation. In

particular, a new possibility for influencing the power characteristics

-61-

yr .- .,~ *. -

• l•P •i LT••:• - -------, . .. ..

of thermoelectric devices, the useful power (the temperi.ture drop at the

junctions) arid the generator efficiency or the cold productivity and the

cooling coefficient of refrigerating devices and conditioners is opened up.

As is well known [28], the temperature profile in the material of a

monolithic thermocouple is described by the following equation:

= T ,- 7"-7'1 Q:- (10)

where Qv is the internal heat generation in the material of the branches

(Joule heating), 6 is the height of the thermocouple, A is the thermal

conductivity of the material of the branches (average for the p - n pair);

T2 and TI are respectively the temperatures of the hot and cold junctions.

It is apparent from the expression given above that the temperature

profile has a non-linear character. The non-linearity of the temperature

profile along the height of the thermocouple is determined by the magnitude

of the internal heat generation. The Joule heat which is generated within

the branches when the electric current flows through them, increases the

excess heat flow to the cold junction and the temperature gradient, depending

on the dist?'ce from the hot junction to the cold. In this case, less heat

enters the thermocouple from the hot side than leaves it from the cold side.

The difference in heat is equal to the Joule heat generated in the material

of the branches when electric current flows through it.

It can be seen from equation (10) that the shape of the temperature

profile in a monolithic thermocouple depends on the temperature drop at the

surfaces, the height of the thermocouple, the heat conductivity of the

material it is made from, and the magnitude of Joule heat generation.

-62 -

However, in the case of a permeable thermocouple a significantly -,cater

number of factors exert an influence on the shape of the temperature profile

in the branches of the material. The direction of flow has the most influence:

i.e., against the heat flow (from the cold to the hot junction) or in the

direction coinciding with the heat fl•w (from the hot to the cold junctions).

Additionally, the structure of the permeaNe material (finely porous or

perforated) and the heat traisfer coefficients within the branches also

significantly change the shape of the profile.

Y! Figure 16.

J-7/ ,Diagram of a permeable thermocouple.

,•,���.�,�i <1. Coolant,

2. p- type,, 2• j ,3. n - type.

' LL~ I,", r' l _"/ s

When Qbtaining expressions for describing temperature profiles in

permeable thermocouples, we will consider the thermocouple circuit shown

in Fig. 16.

1. Method of Calculating the Temperature Fields

We will initially consider the case when a substance (gas, liquid)

blows through the thermocouple directed from the cold to the hot junctions,

i.e. in a direction contrary to the heat flow in the material of the

branches. We will adopt the following basic symbols: T2 ani t 2 are

respectively the temperature of the material and the blow-through medium

at tle hot side when y = T; and t1 are respectively the temperature of

- 63 -

the material 7nd "he blow-through medium at the cold side when y = 0.

The specific mass velocity of the blow-through medium, pv applies to the

entire surface of the finely porous thermocouple and to the cross sectional

area of the capillaries in the case of perforated thermocouples.

In investigating temperature fields in permeable thermocouples, in

addition to the heat conducting processes it is necessary to consider the

processes of convective heat exchange for the mass of the material of the

branches and the blow-through medium fed through the surface of the pores

or capillaries. This means that the temperature profiles in the material of

the branches and in the blow-through medium will be closely interrelated

within the boundaries of the thermocouple height.

We will consider the unidimensional problem of obtaining temperature

profiles in the material of the by~c~hes and in the blow-through medium

(see Fi-. 16). jWhen the coolant is blown through the permeable wall it is heated up,

extracting heat from the material of the wall. The coolant is heated due to

the gain in the amount of heat passed by thermal conductivityextacin (Fa fromP th aeilo h al Th olati hae det

through an element of the wall, dy, and also due to the internal heat

generated in this volume element (when electric current flows - the Joule heat),

i.e.y-,--- d+ + qv (F - F,,o.")dy, (0I)

where F is the cross sectional area of the capillaries.lrOP

-64

5_51 SC

THIS

PAGEIS

MISSING

IN

ORIGINAL

DOCU viN -1

The constants A, B and C have a somewhat different form depending on the

nature of the thermocouple material: porous or perforated.

From the equations introduced above, it is easy to find expressions

for the determination of the temperatures of the material and the blow-through

medium within the boundaries of the thermocouple height, having the deter-

mined the constants of integration from the conditions of temperature

constancy for the material and the blow-through medium at its surface

(where y =s and y =0). In this case we obtain the following expressions:

T =T + .Cy -A-C (7,1 -- -- C) 21-!- A X

-rU :){exp (B2

{e oxp [ _(B ,4))i _

+ t4 .4x p(- A -2 Tx - +) A ' B ()A

• % - I

*- +) i(+÷--t T--C + "" +--xpbB-- )

S(-- + .,,) [-(B -+ 1)_-- + 2 (17)

,4 2B -A

ULI

where BT C)( --

2( - T6 -Ab

.44'

C . . ..AoP

2 A

52

-66-

For finely porous thermocouples where it is practically impossible to

determine the heat exchange surface, the heat transfer coefficient, (av),

characterizing the heat exchange per unit volume of material in the

thermocouple branches is usually employed. For the case of perforated

thermocouples, where the internal heat exchange surface can be determined

relatively simply, the coefficient of heat transfer characterizing the

transfer of heat through a unit surface of the capillaries is employed.

When calculating the temperature fields based on the relationships given

above, it is pFssible to employ these coefficients for heat transfer which

take into account the various forms of the constants A, B and C.

The differential equations which describe the temperature profiles

in permeable thermocouples, which are blown through in a direction coinciding

with the direction of heat flow (from the hot to the cold ju.%,-tions) and

which are obtained by analogy with the expressions given above for the

opposite blow-through direction [10], have the torm

_____ ' "(19)

dy.-T- AT_ .( __Fr___) d, .

i"0

The general solution of this system can be presented in the following

Oren:

"iB67c-p--- "

- 67 -

The constants of integration Ci, C2 and C3 are detemined from the bound-

ary conditions for the temperature constancy of the blow-through medium

and the material of the thermocouple branches at the surfaces of the

junctions (where y = 6 and y = 0). In this case, the expressions which

describe the temperature profile for the indicated direction of flow,4

take the form:

-- (TIC2-tB ~ 2,j2/ + A - C

e_ p B+')

Sexp (B -- Y• I) L Lap- 2 y I))AC" 2 ,"•el -- -------- _(

(2B + A) ×xj) ( 1 (2+ +

2 C). - ', +

("+ )oexp B()+

-L2,-

±exp~~~ep 1+Y±4+)~ (4÷A

.,. ex p -- B, 2AC.1

whereSrne (22)

A .B

S1. ) -B +' k +p J

Q1

- 68 -

The equations which were obtained for describing the temperature

profiles in the material of the thermocouple branches and in the heat

carrier (coolant) blowing through them, both for the case of blow-through

from the cold to the hot junctions (equations 16 and 17), arid for the

case of the opposite blow-through direction (equations 21 and 22) have a

rather cumbersome form. They can be somewhat simplified in the design

of devices which operate within a fixed range of blow-through medium flow

rates, for the case of set geometric dimensions of the thermocouples andr

in certain other cases when terms of the second order of smallness appear

and can be neglected without detracting from the computational accuracy.

However, it is necessary to note that for the existing multiplicity of

high capacity computers, the numerical solution of these equations presents

no difficulties at all, without any simplification (algebraic).

As has already been noted, in the expressions given abo%!e for determining

the temperatures in the material of the branches and in the medium being

blown through them for flow in both directions, the values of the coefficients

A, B and C have a different form depending on whether the thermocouple is

finely porous or perforated.

These coefficients have the following form:

for finely porous thermocouples:

A ui=~ - c : " -i•:,

for perforated thermocouples:

• , , 69C

- 69 -

2. Analysis of the Temperature Fields

We will now consider the character of the change in temperature pro-

files in the blown-through thermocouples for various directions of flow

depending on the operational conditions for specific examples. Let a

thermocouple with a height of I cm have 25 capillaries per cm2 of surface,

each with a diameter of 0.1 cm. The temperature profiles of the thermo-

couple described above are shown in Fig. 17 a and b for the material of the

branches (solid line) and the medium blown through the capillaries (dotted

line).

,.. ./7 Figure 17. Temperature profiles in/ /, permeable thermocouples.

I --I / "A

Z-

I i./t , j

Fig. 17 a corresponds to the case where the flow direction is from the

cold to the hot junctions, i.e. when the blow-through medium is heated in

the capillaries. The temperature prof' ,,s shown in the figure were computed

from formulas (16) and (17). The temperature profiles for the case where the

blow-through medium flows in the opposite direction, i.e. when the medium is

cooled inside the thermocouple, is shown in Fig. 17 b. These profiles were

computed from formulas (21) and (22). The curves, 1 , in Fig. 17 correspond

-5 2to the small specific flow rate of the blow-through medium of 10 kg/cm . sec,

while the curves, 2, are for a flow rate of 10" kg/cm2 sec. The temper-

atures at the hot and cold sides were taken as 1,O00 and 3000 K respectively,

-70-

while the temperatures at the surface, through which the medium is blown,

and of the blow-through medium, were taken as equal to each other for the

sake of simplicity.

The considerable influence of the flow rate of the blow-through medium

on the curvature of the profile can be seen in Fig. 17. If the temperature

profiles in the material of the thermocouple branches are nearly linear

(analogous to monolithic thermocouples) at a small mass rate of flow, then

when the rate of flow is increased, they bend sharply. As has already been

noted, the bending of the profile is caused by the temperature gradients at

the hot and cold surfaces, thus also the heat entering the thermocouple at

the hot side and leaving it at the cold side. The difference in these heats

is explained by the heating or cooling of the blow-through medium within the

capillaries.

As is evident from Fig. 17 a and b, for temperature equality between the

blow-through medium at the inlet to the thermocouple and the responding

Isurface of the thermocouple in proportion to the movement of the blow-through

medium through the capillaries, this equality is not preserved and the difference

in temperatures between the medium and the material increases. The irrevers-

ibility of the heat exchange arises due to the small heat transfer coefficient

in the capillaries. Calculations based on the expressions given above, as

well as experimental data [28] show that in finely porous systems, this

irreversibility is much less and under specified conditions, approaches zero.

However, in capillary thermocouples the heat exchange irreversibility is sub-

stantially less than in monolithic couples, even for extensive fin cooling

of the junctions.

-71-

41

* ''--4:i•• •?• 'a-•.. • " - - •

The diameter of the capillaries and the number of them per unit surface

also exhibits a substantial influence on the curvature of the temperature

profiles. For an insufficiently large number of capillaries, the internal

heat exchange will not exhibit any influence on the temperature profile in

the material of the thermocouple between perforations. Such a situation was

observed when blowing air through perforated plates from the cold side to the

hot [1O].

The temperature profiles measured in the material of a perforated plate

with 22 perforations per cm2 each with a diameter of 0.5 mm for various mass

rates of flow of the blow-through medium, pv , are shown in Fig. 18. Thi

dotted lines show the results of calculations based on the theoretical rel- 1ationship (13). It can be seen that there is sufficiently good agreement I

between the theoretical and the experimental data.

' ...... ' . . ,,

I 2 ,-,-, - I ,I l ;•""• ,•

I A-2

3-x- 18. ITt i , . ,-

"3 -- p ., • 0. " 1.11 M -• . W -, . -• - . - " - , ".

4, 0.3,

S , .6s3 10-1.

Figure 18. Theoretical and experi- iigure 19. Temperature profiles

mental temperature profiles in a in a perforated wall with a small

' perforated wall. number of perforations.

-72-

4-

~O~4 ...

-4

The results of blow-through of a perforated plate with 10 perforations

per cm2 having a diameter of 0.8 mm ar2 'hown in Fig. 19. As was to be

expected, for a small number of capillaries the bending of the temperature

profile in the wall material was not observed even for large mass rates of

flow of the air. The temperature through the thickness of the wall in this

case changes in accordance with a linear law characteristic of monolithic

walls.

In this way, the features of the temperature fields in permeable thermo-

couples make it possible to influence the thermal flows at the surface of

the thermocouple to a greater or less degree, thus also influencing its power

characteristics. A qualitative and quantitative analysis of such influence

will be given below when considering specific circuits of thermoelectric

devices having permeable thermocouples.

The features of temperature fields considered above for permeable thermo-

couples can also exert a significant influen'e on the method of averaging

the parameters of the materials of the thermocouple branches operating in

the given temperature range [9].

In monolithic thermocouples, where the temperature profile approaches

the linear, the average temperature is located near the center of the thermo-

couple branch. In the case where thermocouples are blown through, a

significant portion of the height of the thermocouple can operate at a

slightly changing temperature and the average temperatL,-e will be located

not in the center but closer to the hot or cold side, depending on the

direction of blow-through.

Taking into account the fact that the properties of many thermoelectric

materials change rather sharply with an increase in temperature, the

-73-

- - 71parameters for permeable thermocouples are to be averaged both for the

temperature and for the height of the branches.

Chapter IV

The Design of Thermoelectric Generators with Permeable Thermocouples

The literature has dealt in adequate detail with generators having

monolithic thermocouples, their design methods, operational analysis and

the structural features of devices for various purposes; in the piesent

work it proves to be expedient to cite the known data. At the present time,

information on the design methods, structural features, etc. of generators

with permeable thermocouples is contained only in periodicals. For this

reason, we shall take up in detail the design methodology and analysis of

I the operation of generators with permeable thermocouples as well as consider

their heat circuits. As has been noted in the preceding chapters, it is

possible to consider two directions of flow for permeable thermocouples

using a liquid or gaseous medium - from the cold junctions to the hot and

vice versa. The direction of the medium flow, either in the direction of heat

flow or vice versa, substantially influences the temperature profile in the

thermocouple material (see Chapter III), thus also the thermal currents at

i } the surfaces of the junction, which in turn has a very great effect on the

operational modes of the generator and on its power characteristics. Under

these conditions, the design methods of such generators will be entirely

different.

- 74 -

S'

1. The Design of a Generator Flushed by a Coolant Flowing From the

Cold to the Hot Junctions

For the case of the indicated direction of medium flow, the temperature

drop at the junction of the thermocouples with any possible heat source

is created primarily due to the removal of heat by the cooling medium within

the permeable thermocouples, and partially (in cases) at the surface of the

cold junctions.

Practically any gases and liquids can be used as a cooling medium. A

fuel or an oxidizer which react with one another upon exiting the surface of

the hot junctions, thereby heating them, can be employed to create the temp-

erature drop at the junctions of permeable thermocouples when operating gen-

erators using combustion products from organic fuels for heating the hot

junctions.

We will now consider a generator with internally cooled thermocouples

and hot junctions heated by combustion products from organic fuels, which

is schematically shown in Fig. 20.

Liquid or gaseous fuel is fed into the device with an insufficiency or

surplus of oxidant. In the operational inode where there is oxidant insuff-

iciency, a mixture of unburned fuel and combustion products exists through

the batteries. The unburned fuel continues to burn in the oxidant which isblown through the permeable thermocouples from the hot to the cold junctions.

With such a circuit, the cooling of the cold thermocouple junctions

can be realized in two ways, depending on the temperature drops at the

junctions necessary for obtaining the requisite useful power.

-75-

S Figure 20. Circuit of a generator with internal cooling and heating

of the hot junctions with combustion products.

In the first place, the coolant can be fed in against the heating flow

and effect combined cooling of the cold junctions. In this case, a portion

of the coolant flow being sucked through the permeable thermocouples, removes

heat inside the capillaries. Another portion of the cooling flow, removing

heat at the surface of the cold junctions, is subsequently utilized as

primary air for oxidizing the fuel, returning the same heat which was removed

from the cold junctions, to the combustion region.

Secondly, the temperature drop at the junctions of the thermocouples

can be created only by blowing the cooling medium from the cold to the hot

junctions. In this case, in order to realize the operation possibilities

of the battery with a large temperature drop at the junctions, the coolant

can be fed into various sections along the length (sectionally).

In both of the described heat circuits, the heat losses from the cold

junction side of the generator is for practical purposes nonexist ent. All

I -I

of the heat is returned from the cooling medium (in the given case, the

oxidant) to the combustion region.

It is assumed in the design of such a generator, that the following

are known: its geometric dimensions, the temperature drop across the junctions

AT, the type of fuel (heat generating capability and composition), primary

Sair flow rate GB tpuLo, kg/kg (d is the coefficient of air surplus or insuff-

• - 76-

can be created only by b~~loigte colnmeimfmthcldoteht

iciency), the initial oxidant flow rate ahead of the batteries GO kg/sec,0

the initial oxidant temperature ahead of the batteries to, °K, and the

specific coolant flow rate through the permeable thermocouples pv, kg/cm 2 sec.

For a known type of fuel and coefficient of air insufficiency (surplus),

the temperature of the heating mixture ahead of the batteries (at x = 1)can

be methodologically determined [227.

Utilizing this method, it is possible to obtain the dependence of the

initial temperature of the combustion products of any organic fuel with a

known basic composition on the coefficient, a, of oxidant insufficiency or

surplus at the inlet to the device. Consequently, for the known initial

data indicatod above for the generator design, it is easy to determine the

initial temperature of the heating flow ahead of the first thermocouples

(where x 1).

The basic equations of thermal equilibria for thE generator with

permeable thermocouples based on Fig. 22 will have the following form.

Due to c ,vective heat removal, heat from the heating gas is transferred

to the hot thermocouple junctions, which can be described by the following

equation which takes into account both the mixing process of the heating flow

and the injected coolant:B (GO• + 1) cvdt•-. P•'r.kb (I x)cz •!t3--:w I

-j-qbd.v i .7(!3 - T..), (24)

where t 3 is the running temperature of the heating flow; b is the generator

perimeter (along the surface of the hot junctions); kI is the ratio of the

c-oss-sectional area of the capillaries to the overall area of the thermocouple.

The heat transfer coefficient, a,, from the heating gas flow to the hot

thermocouple junctions where the medium is blown in through pores or capillaries,

can be computed, for example, from formula (7). The additional specific

quantity of heat q (with respect to the area of the hot junctions of the thermo-

couples) is liberated as a result of the additiional burning of the fuel in

-77-

T 74S

the oxidizer, injected through the permeable thermocouples when the generator

is operating in a mode where a < 1, i.e. when a heating gas containing comb-

ustion products and unburned fuel reaches the first thermocouple: 4

BQ11 0I - (3)(25) (25)

Depending on the coefficient of primary air insufficiency and the rate of Iflow of secondary air olown through the thermocouples, the additional heat

generation can take place at various distances from the beginning of the

battery (from the cross-section where fuel is injected). This distance

can be determined from the expression:............. --x= -,bLUB. (2b(

":'-• • , )(26)

The heat which is trantzferred to the hot junctions of the thermocouples

by convection from the heating flow, is expended in heat removed from their

surface as a result of tnermal conductivity of the material of the branches,

and in Peltier heat absorbed at the surface of the hot junctions:

Ct• bdT) TJ: ý xATTr~,ba. (27)ci~bdx'(z3 -- T.) '1Ikblv • •=T -\ (-• ) -,rMe di" i T . (27)

K F- F.•o),."F F,

The d.fference in the heats entering at the surface of the hot junctions

and leaving the thermocouples at the surface of the cold junctions is ex-

pended in useable power developed by the generator, and for heating the

coolant from a temperature tI at the boundary of the cold junctions up to

the temperature at the boundary of the hot junctions, t 2 :

78

-78 -

...............

° z'k� ATT~bax + )Ibdx (_T) Zk ATTbdx-b(:n-u - 1) "dy V b6 ( -i 1

d = (28)

- , t AT-b. +- pfl,,lkcbdx (12 - ti). (28)

On the cold junction side of the battery, the Peltier heat which is

generated at the surface, and the heat arriving there as a result of the

thermal conductivity of the material of the thermocouple branches, with the

exception of a slight amount of heat, is expended in heating the cooling medium

which washes over the junction s1 rface. The latter slight amount of heat is

returned inside the thermocouples and further in the combustion zone with

the injected oxidant, i.e.:

. , '. •- ~ •l'.'dI/ -- p:,,:c bdx (!t -- t) =

C•"..,,!x ('-,"I /) 2: kbdx (29)-- t ,.d1y = (29)

( ': A\TT bdx -o v.,hcbd.x (Il -1 o). (29)

Having rewritten the equilibrium equations considered here in a form more

convenient for solution, we obtain a system of equations which makes it

possible to determine the temperature distribution of the junctions, coolant

and heat carrier along the lIpigth of the battery, as well as all of its

other characteristics:i3u- •~ 0t~:•--L'1 edt~

al~b dX a dx

,- I) • d il

t.Acb dt, dr:' %. ", - - - , - - T ,.. (33)

-79- (3;)

where z and A are respectively the figure of merit for the material of the

thermocouple branches and the coefficient of heat conductivity of the mat-

erial, which are taken as the averages for the p - n pair. Additionally,

the quantity, z, takes into account the imperfect contact of the thermo-

couples. The coefficient of heat transfer a0 from the cold junctions to

the cooling flow characterizes the irreversible heat loss from a portion

of the coolant which washes the surface or the jundtions. The magnitude of

this coefficient can be determined from the criterion equation (8) obtained

for the case where the medium is sucked through a finely porous surface.

In the solution of the syster, of equations (30) - (34), one equation

is still needed - for the temperature of the coolant at the output of the

capillaries (where y = 6), which is obtained from the expression describing

the temperature distribution in the oxidant flowing in the permeable thermo-

couples (14):t.. -7", ( ) -'Li- k') -- k -C( -. ,).- ..LC) "i" h,( \T" -- C.-i "

L ~ T0.3J!)

of -t-Ie batte s..:0I .

Thus by solving the system of equations (30) - (35), we obtain ex-

presion fordetrminng he tmpeatur ditribtios alng he lngt

of the cold junctions:

(s. " . .' *p: ! ',d,7 ) ( ..', + .

T, = .... , (36) (36)-A A• -:Q-u. , -r i T

of the coolant washing over the surface of the cold junctions: .

. I I

Ii I ... . . . .

+ I -, ,c, ' , '.,r ,,, ,',7) ••

(i. ,, .,• •••

II'I- ,.

•(37)

of the heating gas:

I )I:, T, I-" -- , (3S (,8)

of the coolant at the inlet to the capillaries (where y = 0):

= - C (39) : iof the coolant .t the outlet of tite capillaries:

t2 T 1 + k7 (40)

It should be remembered when carrying out calculations based or' the

given equations, that the running values G;f the temperatures to, T1 and t

are reflected in the relationships (37) - "40). 7or example, in the deter-

mination of the temperature of t.,e neati% ;as in any sectlorn, it is nec-

essary to substitute the tenperature values t., t0 and TV which corr.:.pond

- 81 -

to this section, in equation (38).

The order of performing the calculations for a generator with permeable

thermocouples is as follows. First, the change in the temperature of the

coolant flow along the length is determined from equation (37). After

this the temperatures of the cold junctions of the thermocouples in the

corresponding sections are computed from equation (36). Then the temp-erature changes in the coolart at the surface of the. hot and cold junctionsas well as the temperatures of the heating flow are found from equations

(38) - (40).

The following conventional symbols are adopted for the relationships

given above:

-,A '2" -2p -- A+w,, -.k, (B- 2 -) tAI4-( B-) -A

k -- A- + -I-- Ii -. " '( - 1

\-I " j' -D!

- . .! -. A -j " - - - -

" "-C- C- /,6.;AT"-- 'C.S,

The temperature gradi~nts at the surfaces of the hot and cold junctions

of the thermocouples tak:ng into account the adopted symbols will have the

form:

C. -T . (41)(±•.t .:AC - 2" (AT - C(., "-- ' '): -

(42)

-82-

It follows from these expressions that the temperature gradients at the

hot and cold sides of the batter'y do not depend on the distance along the

battery and are constant over all its length. The rate of flow of the medium

being blown through them exerts the primary influence on the magnitude of the )C

temperature gradients.

An expression for the determination of the temperature of the heating

flow along the length of the battery qan likewise be determined from equation

4). If equation (38) holds true for the case of generator operation with

an initial coefficient of oxidant surplus (as well as for the deterniination

of the requisite initial and final heating flow temperatu,'es), then it is

possible to obtain the temperature profile of the heating gas from equation

(30), taking into accouirt the additional heat generation when the unburned

fuel is burned up in the operational mode where a 1. In this case, we

obtain the following expression:

-. (,r --- 1 - --

S* "t I I T -L- ' I- - -

(43)

In this fashion, by. means of the -,uations introdurced above, the

distributions of all temperatures (oi unctions, coolant and heat carrier)

along the length of the battery can be determined. The fuel consumption

which provides for the obtained temperature distributions, can be easily

dete-mined from a simultaneous solution of equations (38) and (43).

Additionally, thp fuel consumption can be determined from the equation of

overall heat equilibrium of the generator considered here:

-83-

&-*~.*++II

7

(;I) (44)

The system of equations (37) - (44) makes it possible to carry out

a complete thermal design of the generator, whose hot junctions are heated

by the combustions products of an organic fuel, where the temperature drop

at the junctions is created by blowing a coolant through the permeable thermo-

couples from the cold to the hot junctions.

The efficiency of this generator in the most general case is computed

as the ratio of the obtained useful electrical power to the quantity of heat

gnerated during the combustion of the fuel, i.e.:

_ N (45)

All possible heat losses including also the heat loss with the exhaust gases

are taken into account in this determination of the efficiency of the device.

If one takes into account the fact that the heat of the exhaust gases

following the generator can be utilized in some other heat-consuming device

or in a second stage generator with lower temperature thermocouples, based

for example on the thermal circuits of Fig. 5 e and f, then the efficiency

of the heat-to-electrical energy conversion process itself in the device

considered here can be evaluated having taken into account the thermoelectric

conversion efficiency as the ratio of useful electric power to the heat

passing through the surface of the hot junctions:

(46)

-84 -

IV1

where P'2 is the heat absorbed at the hot junctions as a result of the

Peltier effect.

Some results of a theoretical analysis of the operation of the gen-

erator considered here, which were obtained using the given method for its

design, are gi- , below. To analyze the influence of various factors on the

power characteristics of the generator, design variations were run through on

the "Promin'" computer.

In the design variations, the following quantities were given and

remained constant: the average characteristics for the p - n pair of

the material of the thermocouple branches z = 0.5 * 10-3 1/0 K and

.= 0.01 watts/cm * 0K; the diameter of the capillaries, d = 0.1 cm and

the number of them per unit surface of the battery z1 =25 holes/cm2 ,

which determined the values of the quantities:

F F- F opkFF =0.196 and k - F = 0.804;

the physicdl characteristics of the cooling air X0 = 2.7 • 104 watts/cm •K,

C = l03 watt-sec/kg.deg, Pro = 0.71, 1o = 1.8 • l0-7 kg/cm • sec; the

initial temperature of the cooling air to = 3000 K; the perimeter of

the battery b =10 cm, as well as the geometric Aimensions of the channel

for passing the coolant. It was assumed that • generator is operated in

the maximum power mode, i.e. for m = 1.

The fuel was assumed to be natural gas with a heat -:..=cating capacity

of QH = 0.485 • 108 watt • sec/kg • deg, and the magnitude theoreticallyP

necessary for complete combustion of the air quantity Lo = 16.76 kg/kg. The

dependence of the initial tempt.'a'%ure of the ccmbustion products, t3 , on

the coefficient of oxidant surplus or insufficiency, as no " . can

- 85 -

be easily obtained under these conditions.

In accordance with the method set forth here for generator design,

the givens are the geometric dimensions of the battery and the temperature

drop at the junctions of the thermocouples, (i.e. the useful electrical

power), for a known initial flow rate and temperature of the coolant. In

the calculation process, the distribution of the coolant temperature to, the

hot and cold junction temperatures T2 and TV, as well as the temperature

distribution t 3 of the combustion products for a known heat transfer coeffi-

cient a, from the hot side which is necessary for assuring these conditions

is determined over the length of the battery.

The finding of the fuel consumption from a simultaneous solution of

equations (38) and (43) or by using the dependence of the intial temperature

of the fuel combustion on the coefficient of oxidant surplus, presupposes

that the temperature distribution t 3 of the hot gas over the length of the

battery, which is calculat:d from formula (43), will be satisfied for the

calculated conditions.

Under the conditions described, the necessary initial temperature t3

of the fuel combustion products can be assured for the case of two different

operational modes of the device: for fuel combustion at the generator inlet

with an insufficiency of primary oxidant and combustion with an excess of

oxidant. The initial coefficient of oxidant surplus (insufficiency) changes

along the length in connection with the injection of a portion of the

oxidant through the permeible thermocouples alone the length of the battery

in the combustion region.

If the generator operates with an oxidant excess fed in at the inlet,

-86-

"then as the combustion products move towards the exhaust, they are diluted

by the injected coolant, reducing its own temperature not only because of

the heat removal to the hot junctions of the thermocouples, but also due

to the physical mixing with a colder cooling medium.

In the case where the requisite initial temperature of the combustion

products is assured by the fuel combustion with a d~Ficiency of primary

oxidant, the oxidant feed through the capillaries promotes the generation

of an additional quantity of heat along the length, due to the further

burning of the unburned fuel ahead of the first thermocouples.

.. .. ./ Figure 21. Dependence of fuel consumption B

........... .......... on the blow-through velocity of

the oxidant pv

The dependence of fuel consumption B on the mL•s rate of flow p v

of the oxidaoit blown through the permeable thermocouples in a generator

having a length of 30 cm, at whose junctions a temperature drop AT = 5000 K

is maintained and for a height of the thermocouple branches of 6 = 1 cm,

is shown in Fig. 21. However, for these conditions the change in the

coefficient of oxidant surplus (insufficiency) a, along the length of the

battery, 1, is shown in Fig. 22. As can be seen from these figures, the

operational mode of the battery during the combustion of fuel with a deficiency

of primary air re .,ires less of a fuel expenditure to obtain the same useful

electrical power than the operational mode for an initial oxidant surplus.

The circumstances noted above are easily explained by the fact that the

-87 -

- -~~1'*-A

operational mode requires a much greater flow rate of combustion products

with the requisite initial temperature to maintain the necessary temperature

of the mode when mixed with more cold air along the length of the battery.

This air which is injected through the permeable thermocouples is necessary

to maintain the designed temperature drop at the junctions.

In the operational mode of a generator with fuel combustion for an in-

sufficiency of primary air (a < 1), the reduction in the temperature of the

heat carrier due to intermixing of the colder cooling medium (oxidant)

injected through the capillaries, is compensated to a certain extent by the

additional heat generation during the further burning of the fuel unburned

in the primary air. In this case, the fuel consumption will be less in the

mode of operation where a < 1, other conditions being equal. In the given

case, the front section of the battery serves as a burner device. With a

?I,

Figure 22. Change in the coefficient of

" ... oxidant surplus B along theS"•--length 1 of the thermo-

S,,battery.

reduction in the quantity of injected oxidant, this portion increases and for

1-4 2.Ia flow rate pV = 5 10 kg/cm 2 sec amounts to 2/3 of the generator

length.

The efficiency of this generator at a power of 75 watts (constant

temperature drop at the junctions AT = 500Q K) changes as a function of

the specific rate of flow of the coolant blown in through the pemeaole

88 I

thermocouples according to the curves shown in Fig. 23. It can be seen E

from the figure that the efficiency at which the given useful electrical

power • rained from the generator increases according to the extent of

reduction in the flow rate of the coolant blown through the thermocouples.

Fia. 24 shows the change in the temperatures of the coolant t0,

washing over the surface of the cold junctions, T2 of the hot junctions of2*

the thermocouples and the initial temperature of the combustion products t 3

in the section x = 1, i.e. at the inlet of the combustion products into the

generator, t 3 being necessary to assure the temperature to and T2 . It is

apparent from the drawing that for the cooling mode considered here ('he ratio

of the medium blown through the capillaries to the total quantity of coolant

reaching the cold junction is equal to 0.58) in the region of small flow

rates of the injected medium, the coolant is heated up to significant temp-

eratures, which entails an increase in the operational temperature level of

the thermocouples, and consequently an increase in the initial temperature

of the combustion products. However, the difference in temperatures between

the hot junctions and the healing flow decreases in this case. This

phenomenon can be easily explained by considering Fig. 25, in which the

dependence of the ratio of the temperature gradients at the surfaces of

the hot rnd cG'd junctions of the thermocouples on the rate, pv, at which

the cooling medium flows through them is shown.For low-fl'w ve'bcities, the ratio U-)T (d y is not large

dy 6'yy=and grows sharply witn an increase in the coolant rate of flow through

the capillaries. This condition in turn means that from the side of the

cold junctions much mnre heat ar-ives for heating the cooling flow at small

- 39 -

injection velocities than in the case of large pV.. Within the limits of

increase for pv , the quantity of heat arriving at the surface of the

cold junctions as a result of the thermal conductivity of the material of

the thernocouple branches, and expended for heating the coolant, which washes

over the latter, can approach zero. In this case, the cooling flow will be

''-.o,,A .... . . .. ..

" " Figure 23. The dependence of the

thermal battery efficiency

n on the flow rate of the

. . oxidant, pv blown through

the capillaries.

Figure 24. The change in the temp-erature of the heat carrier,

.. .. ... coolant, and junctions as

... a function of the oxidant

._ .. Srate of flow pV in the

cross-section x = 1.

heated up primarily by Peltier heat liberated at the surface of the cold

junctions, which is likewise not very great due to their low temperature.

This heat causes very rapid cooling which is clearly visible from Fig. 24,

where for large injection velocities of the coolant, its temperature before

the last thermocouples (counting from the inlet of the cooling flow) is

almost not distinguishable from the initial temperature.

When the injection velocity of the coolant is increased, the heat outflowA

due to the thermal conductivity of the material of the branches from the hot

junctions of the thermocouples increases sharply. This heat is expended

primarily in heating the large quantity of coolant blown through the permeable

90-

LLthermocouples to a rather high temperature. In this case, the initial temp-

erature of the combustion products also begins to increase with an increase

in the injection velocity of the cooling medium.

pif........ , Figure 25. Dependence of the ratio of the7I- .- _i'temperature gradients at the junctions

! ' • fdT • (dTdyT"y=6"• dy )y=O on the oxidant

rate of flow, pV

The change in the coefficient of oxidant surplus (insufficiency) g

" Ialong the length, 1, of the generator for specific oxidant flow rates

through the capillaries, and the temperature drop at the junctions

AT =800 0 K is shown in Fig. 26.

-, -Figure 26. The influence of the flow rate ofthe injected oxidant on the coefficient

-.. . •of oxidant surplus, B.

- I,

This graph like,,,.. . nfirms the expediency of generator'operation in

-91-

a mode with an initial oxidant insufficiency. The dependencies o shown in

this drawing assure the same temperature mode of generator operation, but

at substantially different fuel consumptions.

The dependence of the efficiency of the generator on the injection

velocity of the coolant shown in Fig. 23 was calculated from equation (45).

As has already been noted, this equation takes into account the reduction

in generator efficiency due to heat losses with the exhaust gases.

The loss of heat with the exhaust gases is a determining factor both

in generators with permeable as well as in generators with monolithic thermo-

couples. If generators with permeable and monolithic thermocouples operate

in the same temperature range and with the same temperature drop at the

junction, then their efficiency computed from formula (45) will be the same

under conditions of complete heat recovery from the cold junctions in both

devices.

In contrast to generato'rs with non-permeable thermocouples, an increase

in the efficiency of generators with permeable thermocouples can be obtained

by creating a greater temperature drop at the junctions (obtaining a greater

useful power) due to higher rate of heat exchange when a coolant is blown

through the capillaries. In this case, the coolant flow rate will also be

substantially less than in devices with monolithic thermocouples, even where

the cold junctions of the latter make extensive use of cooling fins.

A comparison of the operation of generators having permeable and non-

permeable thermocouples without taking into account the loss in heat with

the exhaust gdses occasions certain difficulties due to the lack of clear-

cut boundaries within which it would be possible to place both generators

and assure similar conditions for their operation. In fact, the efficiency

of generators with monolithic thermocouples is computed from the well-known

-92-

... ....

relationship [6]:

,.+ U , r , +x + + (47)

i.e., the useful electrical power is related to the quantity of heat enter-

ing the thermocouples from the hot junction side, or to the quantity of

heat exiting at the surface of the cold junctions plus the useable power.

In a permeable thermocouple, these heat quantities differ sharply from one

another owing to the removal of heat to the coolant within the thermocouples.

For this reason, the equation introduced above is not justified for the case

of permeable thermocouples.

g n

t n

Figure 27. The ,alues of the temperature12CO > .. gradients at the junctions 7

__ - of monolithic and permeable_... ---- thermocoupl es.

P ',. '27.

The values of the temperature gradients at the surfaces of hot and

cold junctions.of monolithic and permeable thermocouples are shown in Fig. 27

as a function of the temperature drop at the junctions for a coolant flow

rate through the permeable thermocouple of 10-' kg/cm2 sec. As can ".,

seen from Fig. 27, the temperature gradients at the junctions of permeable

thermocouples differ quite sharply. Here the ratio of the temperature

gradients at the hot and cold junctions for the given permeable thermocouple

-93-

'- * .ilk

7"

depends only on the flow rate of the coolant through the capillaries. An

increase in the flow rate of the coolant through the capillaries causes a

large increase in the difference of magnitudes of the temperature gradients

at the surfaces of the cold and hot junctions of the permeable thermocouple.

Consequently, if the efficiency of the permeable thermocouple is calculated

similarly to t.:e monolithic (the dotted line) according to formula (47),

then in the calculation of the quantity of heat exiting at the cold side, it

will be much higher than for the case of the calculation for the quantity of

heat entering the thermocouple from the hot side. If it is assumed that theheat removed by the coolant in the thermocouple is returned to the heating

flow and can be furthe- utilized, then the efficiency of the permeable thermo-

couple, characterizing the conversion efficiency :)4 thermal into electrical

energy can be computed fr.,m formula (47). In this case, the useful power is

related to the quantity of heat exiting the cold junction side plus the quantity

of extracted power.

- / Figure 28. The dependence of inergy

conversion efficiency on the

1 '"temperature drop at thejunctions of the thermocouples.

In Fig. 28 the relationships of monolithic and permeable thermocouples

to the temperature drop -:.; the junctions are shown as calculated from

formulas (47). The relationships shown.in.this'figure are of purely theoretical

-94-

interest. In the comparison of the operational efficiency of generators

-. with monolithic and permeable thermocouples, intended for any sort of concrete

operating conditions, an individual approach is necessary which takes into

account all the features of the device being designed.

2. Design of a Generator Where the Heat Carrier Blows Through From

the Hot to the Cold Junctions

The circuit of a thermocouple operating as a generator of electrical

power and having a heat carrier blown through from the hot to the cold

junctions is shown in Figure 29 [13].

A hot heat carrier at an initial temperature of t 3 blows through

capillaries made in the branches of the generator thermocouples. In the

given case, heat is delivered to the battery not only through the surfaces

of the hot junctions of the thermocouples, but also within the capillaries.

Such a battery can be employed, for example, to utilize the heat of combustion

products exhausted from any kind of heat-utilizing plant. Naturally, under

these conditions the flow rate of the hot heat carrier and its intial temp-

erature ahead of the batteries are given.

Let us assume that the battery is fabricated from permeable thermocouples

having the same geometric characteristics and its dimensions are known.

This means that where the average perameters of the materials of the thimo-

couple- branches are known, its internal electrical resistance, r, is

known. If the electrical resistance of the load, R, and the requisite

useful power consumed in it are known, then it is possible to find the

temperature drop which should be maintained at the junctions of the given

-95-

711

battery from equation (6):

T = ,,+ (48) (48)

Heat carrier

I, ,',,,,,.•'. •Figure 29. The circuit of a thermocouple '

.. ,, ,, ,where the heat carrier blows

"gi I: I. I.h, , I

.)-•,.,'if:: ... •;through from the hot to theI• • X ,, Icold junctions.'I coolat

This drop is created by the cooling of the heat carrier from an initial

temperature t3 ahead of the thermocouples to a temperature of the cooling

flow to, i.e. we r

or, simplifying this expression we obtain

Pv:,P. k cpkbi (91 -- 1t) -- - 17, -- .bl-:- 49 (49)'-

(49)

where n~ is the Peltier heat generated at the cold junctions of the

permeable thermocoupl es.

The temperature of the hot heat carrier is reduced from the side of the

hot junctioas of the permeable thermocouples due to the absorption of the

Peltier heat at the surface .of the hot junctions and also die to the removal

of heat as a consequence of the heat conductivity of the material of the

9-96-

l:hermocouple branches, i.e.

pv,,ckb!(t--t) , "1- 7'2kb0 + bl(•L) (50)(50)

From exp;-essions (49) and (50) it is not difficult to find the temperature

of a heat carrier at the input to the capillaries (where y = s), by -!

calculating the temperature gradient at the surface of the hot junctions

from equation (21):

y3'r/ t t) 2A.• , -.sr - m

6(n + 1) + 6 1) T

+(B -) (AT T 1 tIC) 4 AC.

from this equation we obtain:(51)

A2 .., ka

where a i. -p Ak2=2B .B . 6.,-()•: ,.1 6 rn; -, 1) 2 - - -,.

- B --

AI= ,t; ('e p B+

22

" --r) °-'•p-r r• - A- -T A

k:

( •i £ I-+.)exp( A46

- 97 -

2

Y ex+ (B AI 6' .... -ý! up'+ A6._+"+++-.++_ +• <+:'.++,,:+

A

The temperature of the heat carrier tI at the outlet of the capillaries

on the side of the cold junctions can be determined from equation (22) for

the condition y = 0. Neglecting terms of the second order of smallness in

this equation, we obtain an expression for the temperature of the neat

carrier at the surface of the cold junctions:"1 A o•(B+ )

•;, t :.= T1 - C +I 2 • 2

ha ot (52)

A 2

i It is more expedient to maintain a high temperature of the hot junctions

in generators (see Fig. 29), which permits the maximum utilization of the

heat of the hot heat carrier by creating the maximum temperature drop atJ

the junctions of the thermocouples. The maximum value of the temperature

of the hot junctions can be obtained by equating it with the temperature of

the heat carrier at the surface of the hot junctions (where y = p), i.e.

when T2 = AT + T I t 2 , or taking expression (51) into account

T, : -. (33) (53)

having substituted this in the expression for the values of the coefficients

k2 , k3 and k4 , we obtain an equation for determining the temperature of the

cold junctions of the generator being considered:

fI':::' t T (.- • -1 L)~ 2 'AT) --

I2(I 31 (54)_a_ . ) "+ C

-/IT,-98

-98 -

In such a manner, for a given initial heat carrier temperature t3 and I

temperature drop AT at the junctions of the thermocouples, it is possible

to determine the temperatures T2 of the hot and T of the cold junctions

of the batteries and the temperature of the heat carrier at the input to

the capillaries t 2 and at their outlet tI from equations (51), (52) and (54).

After this it is necessary to carry out the calculations for the cooling

system which makes it possible to maintain the given temperature drop at the

junctions of the thermocouples within the design temperature range.

It follows from equation (49) that the Peltier heat generated at the

junction surfaces of permeable thermocouples, the heat reaching the cold

junctions due ;.;, thermal conductivity of the material of the branches, and

the physical heat of the heat carrier leaving the surface of the cold

junctions at a temperature t, is removed from the side of the cold junctions

of permeable thermocouples by the external coolant flow. These are the three

components of thermal flow from the surface of cold junctions of permeable

thermocouples, which should be dissipated by the coolant flow washing over

their surface externally.

There is no information in the literature on the coefficient of heat

transfer from a hot permeable surface to a cold external flow when a hot

heat carrier is blown through the permeable surface. However, if it is

assumed that the coefficient of heat transfer in the case under consideration

is determined from the equations obtained for the case where a cold medium

-is injected into the hot heating flow, specifically in accordance with

formula (7), then the quantity of heat removed in this case can be determined

in the following fashion:-1 *-r _____

c (TI f ir T1k. (55)

- 99"-

.1

It is apparent from equations (49) and (55) that in the determination

of the heat transfer coefficient from formula k7), it is additionally

necessary to also take into account the increase in the temperature of the

cooling medium due to the physical heat of the intermixed heat carrier which

exits the surface of the cold junctions of the permeable thermocouples. If

the initial rate of flow of the coolant and its temperature at the ;nput to

the thermocouples are known, then it is possible to write the following

equation for thermal equilibrium:

(G -- vjjb): G ,., - 1 pv.c,,kib1 (1, to) +a+ bl (Tir1 -), (56) (56)

I to)or taking into account expressions (44) and (55).

(Onx + pv.. 1bI)cpot)- G• c '"

Pt'&CPrklbl (I1 - :•o 6(m ")) AT 1 .

Relating the initial coolant rate of flow to the area of the generator

and dividing both parts of equation (56) by pVYprklbl, we obtain an

expression for the final temperature of the cooling medium

t3 + 0.5~- .___ftV Dk Cl~r onZp/ 6( - 1)( - )C . (p5 ) ) iS .

P('•- + i) "÷"o0,

(57)(57)In this fashion, knowiug the final temperature of the coolant it is

possible to determine its average temperature over the length of the gen-

erator and find the coefficient of heat transfer for the design mode from

equation (44):

(,-) (58)

-100-

- The magnitude of the heat transfer coefficient a, computed from this ex-

pression can be realistically assured by the choice of the necessary vel-

ocity of the basic cooling medium flow, which can be determined from equation

(7) or from the other equations for the determination of the heat transfer

coefficient when the medium is blown through the permeable wall. In such

a generator, similar heat exchange conditions at the surface of the cold

junctions can be realized by changing the cross-section of the channel for

passing the coolant at its given initial flow rate.

Consequently, the system of equations which is obtainied makes it possible

to completely carry out the calculations for a generator with permeable

thermocouples through which a heat carrier is blown from the hot to the

cold junctions.

The efficiency of such a generator is defined as the ratio of the

useful electric power to all of the expended heat:

p. P.c,)•kbi(ta-tI") kn(i-- 1) pz•.cp.! tin !)(:3-4•)(59) (59)

This expression likewise takes into account the heat loss with the exhaust

gases.

* To evaluate the efficiency of the conversion process of electrical

into thermal energy, it is possible to utilize the expression without taking

into account the influei.ce of heat loss with the exhaust gases:

- ri I) p4cVI (mn + I)(60 ) (60)( (60)

A comparison of the operational efficiency of generators having mono-

lithic and permeable thermocouples, at the present time presents certain

-101-

_•; ... . -; ." I z

difficulties due to a lack of adequate bases for methods of comparison. A

If the attempt is made to compare these devices by assuming that

batteries with the same geometric dimensions operate with the same temp-

erature drop at their junctions, and that the flow rate of the heat carrier

and its temperature ahead of the batteries are the same, then the efficiency

of a non-permeable battery will have the following form, u .tig the same

conventional symbols:1o1 1,)T P- - •7 (61) ,= On 0. + 1)(-. (61)

This expression, just 3s (60), does not take into account the heat loss

with the exhaust gases. Here'P 2 Hn is the minimum possible temperature of

the exhausting combustion products, equal to the temperature of the hot

junction for a non-permeable battery.

To compare the efficiency of the devices considered here, dividing

expression (60) by (61), we obtain,__'~ = k- -- T, (2

,,,.., (62)

The temperature of the heating gases following a non-permeable

battery for the given condition of temperature equality of the hot junctions

and the heat carrier at the outlet can be easily determined from the

thermal equilibrium at the hot side:4 %T

.):,._k c.,bl (t• - - T 2,,,.) = _ z ý: , 7.- ,?:,,.bi --'63-~ ~ va~-. (63)

WA - '0,5 - bi. (63)+ ~ ~ ~ r bT-,5€(+ I)'

whence fs3 p". 'c[ 1-0.5 (,\l +.2im k (6.i) (64)

- 6(+ 1)

-102-

It can be seen from equations (59) and (60) that the efficiency of a

permeable generat.e' taking into account the heat loss with the exhaust gases

can be exr,.s.•ed in the following manner:

1a--f • (65) . (65)1310

For a generator with monolithic thermocouples, the efficiency can be

expressed on analogy with a generator having permeable thermocouples, as:

13- ,,(66) (66)

(herr m'-. .onventional symbols are the same as for permeable thermocouples).

The relationship between the efficiency of generators having monolithic

thermocouples and those which are permeable, in accordance with equations

(62), 165) and (66), has the form

_ =k (.k< 1). ,671) A.)

* Consequently, .for the conditions of comparison considered here, a battery

with permeable thermocouples will be less efficient than one with monolithic

couples.

This circumstance is justifiable only for the Aata from rather restric~ted

conditions, when the same temperature drops at the junctions of thermocouples

are assured in both cases by the hot and cold flows which have the same

initial and final parameters.

However, this is observed up to a set value of AT. In fact, in

batteries with both permeable and impermeable thermocouples, which operate

in the same temperature range of the heat carrier (t 3 - to), the temp-

erature drop at the junctions can incr2ase up to the set limit. The

= 103 -

" . ." . ' ___ ', -

increase in the temperature drop at the junctions of the thermocouple

causes an increase in the Peltier heat which is absorbed at the hot junctions,

and an increase in the heat removed from them due to thermal conductivity

of the material of the thermocouple branches. In this case, if the Peltier

. heat which is absorbed at the hot junctions is nearly the same in both cases

(depends on the amount of empty space in the material of the branches, i.e.

on the porosity or the capillary coverage), then the quantities of heat

which are removed because of the thermal conductivity of the materials of

the branches in monolithic and permeable thermocouples, differ sharply.

In a battery with non-permeable thermocouples, the temperature profile

differs insignificantly from a straight line (see Chapter III), i.e. the

magnitude of the heat flow will increase proportionally to the magnitude of

the temperature drop at the junctions of the thermocouples. In a battery

with permeable thermocouples, the temperature profile along the height of the

thermocouple is very sharply bent, and the temperature gradient at the

surface of the hot junctions for a temperature drop at the junctions the

same as for a non-permeable thermocouple will be substantially less. This

difference in heat flows entering the thermoc3uple through the surface of

the hot junctions ipr.ceases with an increase in the flow rate of the

heat carrier blown through the permeable thermocouple. As an analysis of

tht expressions for determining the temperatures in a permeable wall shows,given in Chapter III an increase in the te,,perature drop A, the junctions ,

causes the temperature gradient at the surface of the junctions of a

permeable then,r-icouple to grow more slowly in comparison with a monolithic

one. In agreement with Fourier's law, this determ4nes smaller heat flows

1-104 -

from the hot junctions in the permeable thermocouples.

An analysis of equations (50) and (63) makes it possible to clarify i.the redistribution of the influence of the absolute values of the mag-

nitude of Peltier heating and the magnitude X(-Z-y)y=, on the reduction of

the heat carrier temperature. Consequently, in non-permeable thermocouples,

the heat which is removed due to the thermal conductivity of the material

of the thermocouple branches in terms of the absolute magnitude greater than

in a battery with permeable thermocouples, and the influence of an increase

in the temperature drop at the junctions on the increase in the heat flow

leaving the surface of the hot junctions in non-permeable thermocouples, is

likewise greater than in permeable ones. This means that the maximum temp-

erature which it is possible to achieve at the hot junctions of non-permeable

thermocouples with an increase in AT, other conditions being equal, will

fall off significantly faster in comparison with permeable thermocouples.

For this reason, a battery with permeable thermocouples is capable of

operating with a significantly greater temperature drop at the junctions

than are monolithic thermocouples.

Thus, equation (67) is justified only up to a set magnitude of AT,

which is achieved in monolithic thermocouples (the value AT is the max-

imum possible within the given range t 3 -tH). ýlr a further increase

the efficiency of such a device will be higher than the maximum possible

ef'Iciency of a battery with monolithic thermocouples.

Consequently, the method given here makes it possible to carry out

calculations for all of the thermal characteristics of a battery throug:.

-105 -

which a heat carrier blows from the hot to the cold juncations.

We will analyze the operation of a battery which is operating in the

mode considered here on the basis of an example of a specific device, cal-

culated in different design variants ior changes in several parameters. For

the design variants, it was assumed that the physical properties of the heat

carrier and cooling flow are the same and equal respectively to: U = 2.4 x

x 10-7 kg/cm" sec; Cp = 10 watts x sec/kg • deg; X =3.8 - 10 watt/cm• deg.

The average characteristics of the material of the thermocouple branches

are z =0.5 • 1- 3 deg- and X = 0.01 watt/cm • deg. The diameter of theF r

capillaries were taken to be 0.1 cm and the the coefficients kI FF - F

0.196 and k 10P = 0.804, which corresponds to 25 capillaries perF

cm2 of battery surface. The ratio of the load resistance to the internal

resistance of the battery was taken as m = 1, the temperature of the hot

heat carrier ahead of the battery t 3 15000 K, and the initial coolantHtemperature to 3000 K.

Figure 30. The temperatures of thermocouple

junctions and the blow-through heat- ' .- •' heat carrier as a function of the

temperature drop maintained at the

junctions.

The temperature of the junctions and the temperature of the neat

carrier entering the capillaries and upon leaving them are shown in Fig. 30

as a function of the temperature drop at th, junctions of permeable thermo-

couples, computed for a heat carrier flow rate through the capillaries of

pV = l0 kg/cm2 • sec.

-106-

However, for the sake of comparison the temperature relationships at

the junctions of a non-permeable thermocouple (dotted line) shown here,

which will be at the same initial temperature as in the case of a permeable

thermocouple for the same rate of flow of the heating gas. *It c.n be seen

from the drawing, that it is possible to obtain much greater temperature

drops at the junctions in a permeable thermocouple than in a monolithic

thermocouple, other conditions being equal. For the given case, the maximum

possible useful electrical power derives from a generator with permeable

thermocouples will be 1.2 times greater in comparison with a generator having

monolithic thermocouples. In this case, the weight of such a battery owing

to the presence of the capillaries will be almost 20% less than a battery

having monolithic thermocouples.

.. T4,

2'1'II . ,Figure 31. The influence of the temp--- , .erature drop at the junctions

on generator efficiency.

Ok. I_The dependence of the efficiency of the battery considered here on the

temperature drop at the thermocouple junctions is shown in Fig. 31. As can

be seen from the figure and formula (62), the efficiency of a battery with

non-permeable thermocouples without taking into account the heat loss with

the exhaust gdses at any temperature drops. across'the junctions,.is higher

than the efficiency of a battery with permeable thermocouples for similar

operational conditions. This is easily explained by the fact that for the

same AT at tne junctions of the thermocouples (almost the same electrical

powers), the temperature gradient at the cold side of the permeable

battery, and thus the heat losses from the surface of the cold junctions,

- 107 -

are significantly greater than for a battery having monolithic thermocouples.

The interrelationship of the efficiency of batteries with permeable

and monolithic thermocouples, computed taking into account the heat los.

with the exhaust gases, follows from (67) and is determined only by the

porosity for the selected method of comparison. However, if one considers

thermobatteries not of the same geometric dimensions as in the given case,

but of the same weight, i.e. the permeable thermobattery is taken to be

larger by the amount of the er,,.ty space volume, then the efficicncy of

both batteries, taking into account the heat losses with the exhaust gases,

wili identical for any "..at carrier flow rates and temperature drops at

the junctions under conditions of complete heat recovery in these circuits.

However, a battery with permeable thermocouples is capable of generat-

ing a greater useful electrical power than a battery of the same geometric

dimensions with monolithic thermocouples.

Figure 32. The deperdence of th, heat transfer coefficient a at thecold junction side on pUo/Pv kI.

"" W V

Figure 33. The Influence of tze ratio pUo/pv k on the average temperatureof the coolant flow t.cP

0

The coefficient of heat transfer • on the cold jonction side and the

average temperature of the cooling flow tcp over the length of the battery-!08 -

Si-4

are shown in Figs. 32 and 33 as a function of the ratio of the specific

rates of flow of the coolant reaching the surface of the cold generator

junctions, and the heat carrier leaving the permeable thermocouples at the

surface of the cold junctions, pUo/PV k1 . It can be seen from these griphs

that for an increase in the ratio pUo/Pv k , at a fixed heat carrier flow rate0 Wlthe magnitude of the necessary heat transfer coefficient a decreases slightly,

but in this case, the average temperature of the coolant flow tcp decreases0

markedly. This is of significance insofar as the generator can operate

with a greater temperature drop at the thermcouple junctions, which means

there is obtained a greater useful electrical power.

3. Two-stage Generator Design

The devices considered above are capable of operating as both independ-

ent generators and jointly in circuits with generators having monolithic

thermocouples and with one ancther. As has already been noted, such combined

circuits make it possible to obtain a more efficient conversion of heat and

nuclear into electrical energy in many cases. By way of example, we will

consider two combined circuits.

The operation or a two-stage generatnr based on the thermal circuit

shown in Fig. 5 f makes it possible to avoid some of the significant drawbacks

of each of the stages when operated independently. In such a circuit, each

of the generators can operate in its own optimum mode. In this case, both

generators operate only with one hot and one cold heat source. The

efficiency of any combined cycle, including the one considered here [27],

can be computed from the formula:

-109 -

k+ 2(I -+ (68)

where n, and n, are respectively the efficiency of the first and second

generator.

In the given circuit, one of the generators can be considered as an

electric generating device of the primary cycle, while the other is considered

a high or low temperature addition to it. Insofar as the values p, and n2

are small, the effect of combining the cycles of both generators is close

to the effect obtained for summing these quantities, i.e. the efficiency of

the jointly operating generators calculated from formula (68) will be almost

twice as great as that for each of them operating independently. In this

case, the magnitude of the coefficient * can be taken as equal to unity, since

when there is complete heat recovery in the first stage, the same quantity

of heat which is delivered to the first stage is supplied to the second stage

of the geaerator.

Not only combustion products from organic fuels, but also nuclear

reactors and radioisotope capsules -an - used in such a combined heat cycle

as a source of heat for heating the hot junctions of the first stage thermo-

couples. Under these conditions, the coolant blown through the permeable

thermocouples of the first stage and heated in them, creating a temperature

drop at the junctions, thereafter is heated to a higher temperature in the

space between the heating surface and the hot junctions. The thermocouple

junctions in this case are heated by radiation from the heating surface and

by convection from the medium cooling the thermocouples in the space between

the heating surface and the hot junctions. The hot gas obtained in such a

manner is utilized as a heat carrier in the second stage of the two-stage

generator.

1- 10 -

During two-stage generator operation on the combustion products of

an organic fuel, the thermal design of both stages can be carried out

in accordance with the methods set forth in the present chapter.

To evaluate the efficiency of a generator employing such a heat circuit,

we will use the results of the design variants for single stage generators

having permeable thermocouples which were given above. Let the useful

electric power of a two-stage generator be 500 watts, where materials with

identical properties are used in both stages, whose characteristics were

specified above. The optimal operational variant of the two stages in this

case, will be the operational mode of the two-stage generator in which the

first stage generates 200 watts of useful electrical power, while the second

generates 300 watts. The efficiencies of these generators, which are defined

as the ratio of +he useful power developed to the fuel consumed for its heat

generating capacity, were respectively 1.03% and 1.55%. The overall efficien-

cy of the two-stage generator calculated in the same fashion was 2.58%.

The primary loss is represented by the heat loss with tt,. physical medium

of the combustion products leaving the device. Consequently, the efficiency

of the device considered here was the same as the sum of the efficiencies

of both generators. The absolute value of the efficiency of a two-stage

generator can be significantly greater when a higher quality material with

a figure of merit z > 0.5 • 10-3 deg-1 is used to make the thermocouple

branches.

The joint operation of generators based on the heat circuits shown in

Fig. 5 b and c (circuit 5 e) can be considered as another circuit for a

combination generator. For example, such a generator can be utilized for

the cathodic protection of gas pipelines.

- 111 -

i .The device under consideration consists of two stages and can be•: | built in the form of pipe walls or a rectangular channel. The first gen-

erator stage with monolithic thermocouples utilizes the heat of combustion

products leaving the generator having permeable thermocouples.

The temperature drop at the junctions of the thermocouples of the

first stage is created by means of blowing a gas over finned or non-finned

cold junctions, which is supplied from the gas pipeline.

Following the cooling of the cold junctions of the monolithic thermo-

couples of the first stage, the natural gas is fed to the "old junctions

of the permeable thermocouples of the second stage through channel 3, and

creates at the junctions of the permeable thermocouples the requisite

temperature drop (Fig. 34) blowing through them from the cold to the hot

junctions. After this, upon exiting the surface of the hot junctions of the

second stage, the gas burns in the air.

I'

-- Figure 34. The circuit of a combination generator

z-..4 -, ,:'(A) with permeable and monolithic thermocouples.

I (A) Gas from the main line.

The air necessary for combustion is drawn in naturally owing to the differ-

ence in the specific weights of the combustion products and the surrounding

medium. For this purpose, the device is set up above the ground surface

on posts 4. Thus, the hot junctions of the second stage located in the

combustion zone can be heated up to a high temperature. A sufficient rate

of heat exhange, which takes place when the gas iF blown through the pores

- 112 -

(capillaries) of the thermocouples, promotes a greater temperature drop

at the junctions.

The combustion products give up a portion of their heat to the hot

jundtions of the second stage 2 of the generator, and thereafter enter

the first stage 1 where they are cooled giving up heat to the hot junctions

of the monolithic thermocouples. Convective cooling of the surface of the

cold junctions of the first stage does not permit such a large temperature

drop across them as in the case for the internal cooling of the second

stage permeable thermocouples. However, the first stage increases the

power efficiency of the generator, cooling the combustion products to a

lower temperature, i.e. reduces the heat loss with the exhaust gases.

The requisite flow rate and pressure of the gas, which can be supplied

directly from the gas line, are regulated by means of an automatic regulating

device 5. The gas rate of flow can be varied depending on the magnitude

of the electric current, or the temperature of the hot junctions of the

second stage, or in accordance with any other parameter.

It is expedient to carry out the combustion process not just at the

surface of the hot junctions of the second stage. Since the heat can be

insufficient to heat the hot junctions of the first thermocouples, it is

necessary to place burner 6 ahead of the second stage to obtain a sufficiently

high temperature at the input.

In the device considered here, the heat losses from the cold junction

side can be eliminated entirely. All of the heat removed from the surfaces

of the cold junctions returns with the heated gas to the combustion zone.

The first and repeated starts of such a generator can be accomplished

-113 -

using an electric ignition device, colocated with bu:,;..: 5. The ignition

device can be placed in operation automatically based on a tem'r~ture drop

in the combustion products.

When the materials of the thermocouple branches of the first and second

stages are specified, it is possible to select temperature drops at the

junctions based on the conditions for most efficient operation of these

materials. The optimum generator operation would be obtained when all

thermocouples operate with an unchanging temperature drop at the junctions

of each stage.

Coolant (natural gas) enters the second stage from the first, partially

(pV kliDlH) blows through the permeable thermocouples and burns at the surface

of the hot junctions, and partially (Gr) passes by the permeable thermo-

couples, feeding into the burner located at the generator input, i.e.

G= .-- '

where 1 is the length of the battery of the second stage; D is the

internal diameter of the generator.

To burn this quantity of natural gas, air is fed in by a natural draft,

GB, kg/sec. The air surplus coefficient at the input to the generator will

pv klwDlH Gsbe =1 + since Lo Consequently, for knownSr Gr

rates of gas flow through the burner and the permeable thermocouples, the

air surplus coefficient is known at the input. For this reason, the temp-

erature of the combustion products at the input can easily be found and

the further design of the stage having permeable thermocouples can be based

on the method given in paragraph I of this chapter.

- 114 -

The first stage with monolithic thermocouples is designed for the

known temperature drop at the junctions AT', the rate of coolant flow

(natural gas) G0 and its initial temperature to. Additionally, the temp-K

erature of the coolant at the outlet of the first stage to (where y

the temperature of the combustion products when they enter the first stage

t 3 (when y = 1H) and its gradient at this point become known from the cal-

culations for the second stage.

The heat balance at the cold junction side of monolithic thermocouples

can written in the following form:

a. (TI -- t0) tDdy = Gc d.

From this, the temperature distribution of the cold junctions over the

length of the first stage is determined:

aaD dt (69) (69)

The heat balance can otherwise be written as:

G,, Ddy L_ + ' , A7'TlaDdy. (70) (70)

Determining the temperature gradient at the surfaces of the cold junctions

from expression (10), we find from (70) that:

7T , , i (71) (71)

Equating expressions (69) and (71) to each other, following integration we

obtain the temperature distribution of the coolant over the height of the

first stage with monolithic thermocouples:

- 115 -

0

Ij AT' + 1Vto,+ ru - , .. "' t exp

1z , -. T'( T' 1+ + I

(72) (72)

Knowing the distribution of to , it is possible to determine the

temperature distribution at the cold junctions Ti over the length of

the generator from (69) or (71), thus also the distribution of the

temperature at the hot junctions T•, since = + AT'.

After this, the change in the temperature of the combustion products

along the length of the stage with monolithic thermocouples is caiculated.

Insofar as the flow rates of the combustion products and the cooling medium

in the non-permeable stage are fixed and the temperatures of the heating

and cooling flows in the section y = 1. are known, the temperature drop

which can appear at the junctions of the monolithic thermocouples will

likewise be completely determined. This drop can be determined from the

heat balance equation of the stage with monolithic thermocouples:

,, (tI- 7,) =(T; -- :) 6' (-- (73)

) ((73)

Substituting the temperature values for the junctions from equation (69),

we obtain:

' + 7 +

a

- :°• (74)

In this equr. --, the values of the temperatures tI' and t, as well as the

-116 -

dt'temperature gradient 0 are chosen for the section y = 1 following

the calculation for the stage with permeable thermocouples:

The temperature distribution of the hot gas can be found from the

heat balance equation on the hot junction si6e of the monolithic thermocouples:

Go(Lo -- l) c,,t• =a,:,Ddhj(t' -T..

OTC1oaa

whence " d,3dy=. (75) (75)G( - (t3 + I . )

When carrying out the calculations based on the given equations, the running

value of the temperature of the hot junctions, which is determined from

expression (69) taking into account the fact that Ti = Ti + AT, is to

be used in expression (75).

Thus, using this method it is possible to carry out the complete

thermal design of a combination generator, in which both permeable and mono-

lithic thermocouples are employed.

The overall efficiency of the combined device can be determined from the

relationship

O! = . (76)GoQ. (76)

Such an expi.ssion for the efficiency also takes into account the heat losses

with the exhaust gases.

Chapter V

Thermoelectric Cooling Devices with Permeable Thermocouples

-117 -

1. Refrigerator Design Method

As has already been noted, permeable thermocouples used in the fab-

rication of thermoelectric devices differ from monolithin ones. Owing to

the developed internal heat exchange surface in permeable thermocouples,

the heat transfer between the liquid (gas) blown through them and the solid

material of the branches takes place at low temperature differences, i.e.

almost thermodynamically reversibly.

Such a heat exchange system gives the thermocouple operation its fund-

amental and essential characteristics, opening up the possibility for inf-

luencing the cooling coefficient of the refrigerator or conditioner.

We will analyze the operation of these thermocouples by considering

the temperature curve in the material of the electrodes [12].

The nature of such a curve will change depending on the given operational

conditions of the thermocouple. In rig. 35 are shown Gwo temperature curves,

T = f (y), derived for a refrigerating thermocouple on the assumption that

the temperatures of the hot and cold junctions of permeable and monolithic ,1m

thermocouples are respectively the same, and that consequently the thermo-

electric effects are the same. The thehnocouple is blown through by a coolant,

which is cooled in moving from the hot to the cold junction.

r f

/• /' Figure 35. The character of temp-erature curves in blown-

1 2 T, through and non-blown-4 i% through thermocouples.

Curve 1 which applies to the monolithic thermocouple, is bent upwards

-118 -

"A,

in an arch due to the fact that the generation of jewel heat causes an

increase in the quantity of heat along the y axis, transferred to the coldjunction, thus also increasing the temperature gradient. The cooling co-

efficient n and the cold productivity Qx are expressed in the following

form:

QW Qx Qnt.r t (7-7) (

where Qn.r is tha Peltier heat generated per unit surface of the hot

junction: Itga= and W is the expended power.

Curve 2 is obtained in the transition to thermocouples with internal jheat exchange. lhe position of curve 2 relative to curve 1 can be character-

ized by the increase in the angle a by the magnitude Am. The additional

bending of curve 2 is due to the same cause as the convexity of curve 1,

i.e. the increase in the quantity of heat transferred to the cold junction

along the y axis because of thermal conductivity. In turn, this is connected

with the internal heat delivery from the cooling refrigerant. Thus for a

permeable thermocouple, ' = Q,.where Q is the total cold productivity of

the thermocouple consisting of the heat delivered due to the internal heat

transfer from the cooling refrigerant pvcp (tr - t ), and from the heat

supplied from without to the cold junction Qx:

Q= otP%. -ta1) +Q~ W ~ ~2-~-I. (78) (3

The quantity Qx can be as small as desired or equal to zero. Expression

(78) is distinguished from (77) only by the increase in the angle a.

19 -1

fi

Consequently, e'>E always obtains, other conditions being equal.

For the equal conditions here, it is implied that besides the equality

of the material properties, the flowing currents and temperatures of the

hot and cold junctions of monolithic and permeable thermocouples are also

equal. It is likewise considered that the difference in the temperatures

Suf the filtered refrigerant and the material from which the permeable thermo-

couple is fabricated, is neglectably small. When these conditions are not

observed, qualitatively different results will not result insofar as the

magnitude Am always remains positive. The magnitude of the angle AM is

subject to regulation by changing the quantity of the blown through refrig-

erant, and likewise depends on the temperature mode and the structural

characteristics of the thermocouple.

It is apparent from formula (77), that for very large temperature diff-

4. dernces at the junctions, for the case of very short thermocouples, when the

angle a becomes extremely small operational modes are possible in which

Qx = 0. In other words, for large temperature drops at the junctions (for'

very small branch heights) the cooling thermocouple does not ope,'ate. When '

finely porous or perforated thermocouples are used, such modes can be widely

separated, since even for small magnitudes of the aagle a, it is possible to

preserve a significant quantity for a + Am, having pravided for this the

cooling medium flow rate which is necessary to obtain tte requisice magnitude

of Am.

The qualitative analysis of the operation of monolithic aA. permeable

refrigerating thermocouples given above shows the advantages of the latter

as far as the power characteristics are concerned. For this repson, it is

expedient to quantitatively analyze in detail the operation of a permeable

thermocouple.

-120 -

*; -**A"

5ý7'Z

The thermocouple of a refrigerating thermoelectric device is shown

schematically in Fig. 36. The branches of the thermocouple are provided

with capillaries for passing the cooled medium, which blows through from

the hot to the cold junctions, giving up heat to the material of the branches

of the thermocouples. Depending on t.he application conditions of a refrig-

erating battery having permeable thermocouples, the supply of the medium

being cooled to the capillaries can be realized in two ways. In the first

place, when the cooled medium circulates in a closed loop, its delivery to

the capillaries of the thermocouple branches caa be accomplished through

channels made in the connecting plates of the hot junctions (Fig. 36 a)

Cooling

I,.I',, I ; I !

a a b

Figure 36. Circuits of permeable refrigerator thermocouples. I

In this c)se, heat can be removed from the surface of the hot junctions by

any heat carrier or by natural convection in the case of adequately developed

fin cooling.

In the case where a refrigerating battery with permeable thermocouples

operates in an open ended circuit, the removal of heat from the hot junctions

can be accomplished by a flow of a medium, a portion of which is sucked through

the capillaries of the thermocouples, being cooled iA -hem (Fig. 36 b).

When electric current is delivered to the junction.,, a temperature

-121-

difference is created by the Peltier effect:

V = 'PR + (T,-T2)el. (79) (79)

where I is the current passing through the thermocouple; e is the coefficient

of thermal e.m.f.

In this case, the temperature profile along the height of the permeable

electrode will be bent (see Fig. 35) and the temperature gradient at the

hot side will be lower than on the cold side. Consequently, the transfer

flow of heat due to thermal conductivity from the hot junctions will be !ess

than the transfer flow of heat in the non-permeable thermocouples, other

conditions being equal.

It it is assumed that Qx 0, i.e. there is no heat delivered to the

surface of the cold junction, then due to the Peltier effect only heat will

be absorbed at the cold junctions, which is delivered to the cold junctions

because of the thermal conductivity of the material of the thermocouple

branches and the medium being cooled:

'dT' li- ~elT.=(F F-- ,F..o.[r -'.r-op{ (80)

eIT1 \ d. ,.,_o ' "' , (8,) (80)

During the cooling of the gases, the heat which is delivered to thecold junctions due to the thermal conductivity of the gas is insignificantly

small and in the future we will neglect the second term in (80).

As a result of the Peltier effect, in a non-permeable thermocouple not

only heat is absorbed at the cold junctions which reaches them by thermal

conductivity, but also heat which is extracted from the cooling substance.

Consequently, in spite of the fact that the temperature gradient at the cold

122

side of a non-permeable thermocouple is smaller, the current magnitude

necessary for maintaining the same temperature difference at the junctions

w1l1 be greate- for the same cold productivity, thus also the applicable

power will be greater.

The heat delivered to the thermocouples from the cooled medium and

the applicable power derived from the hot junction side (we neglect the

magnitude Q):Q = + pUc•F~(r - t,). ((81). (81)

The areas of application of permeable thermocouples are limited by

the necessity for operating with very small differences between the temp-

erature of the hot junctions, which should be somewhat higher than the

temperature of the surrounding medium and the temperature of the refrigerant,

fed in through this junction for cooling. In fact, if the refrigerant has

a higher temperature than the hot junction, then it can be cooled beforehand

down to this temperature by thermal contact with the surrounding medium

without wasting electrical power. If the temperature of the refrigerant

returned for cooling is lower than the temperature of the hot junctions and

equal to to, then at the input to the thermocouple, the refrigerant should

be heated to a temperature close to the temperature of the hot junctions,

and thereafter cooled down to the given temperature. In this case, naturally,

it would be necessary to develop the superfluous cold productivity, and the

ratio of the useful cold productivity to t•.e total in this case is equal to

the coefficient ,, -11) , which becomes t t when Qx 0.

The magnitude of the coefficient contrary to the total cold productivity

Sand the cooling coefficient computed from it decreases for an increase in tI.

- 123 -

•, ,-' ,. . - - - , -. ,

V The value of the current necessary to maintain the given temperature

difference at the junctions when a set quantity of the substance being cooled

is blown through, can be determined from (80):

I= zTlaad, T.z,., "2KC j'\ q~e /A B

________(B - -) (-,-1 + ni( - F5 ~ *xp u~)jA Y , .2-,6NKp (4-Tt),

(82)rie

where A=m---- B2 (4,(-f o)

K= ~N

~ I- B - )8exp B) 6-+exA

The temperature profile in the material of the thermocouple branches

necessary for the calculation of the temperature gradient is taken fromexpression (21) when t 2 = T2 .

If the temperature of the medium being cooled ahead of the batteries

and the temperature drop at the junctions are given, then having determined2

the current magnitude, it is possible to find the temperature of the cooled

gas (22) when y = 0:

4 R- 124 -

A )

2 -:i-

I TI - C + N X

x~ +~ f(4 + -T + C (I + A6)] .-C', (83) 1(83)rile

where = J2•1

However, if the initial and final temperatures of the cooled medium

are given for the design, then the necessary current and the temperature

of the cold junction can be found from a simultaneous solution of

equations (82) and (83).

For the current magnitude known from equation (79), it ".s possible

to find the applicable electrical power and the quantity of heat which

must be removed from the hot junctions from (81).

The efficiency of such a battery (the cooling coefficient) is defined

as the ratio of the quantity of heat removed from the cooled medium to

the consumed electrical power:

2. An Operational Analysis of a Cooling Device

We will consider a thermocouple with a surface of 1 cm2, whose branches

are made from solid solutions of Bi2Te3 - Bi2Se3 (n - type) and

Bi2 Te3 - Sb2Te3 (p - type). The average characteristics of the thermocouple

materials for both branches are as follows: x = 0.013 watt/cm. • K;

e = 350 Pv/ 0K; and a = 1150 ohm 1- cm-. The figure of merit for the

material of the thermocouples, taking into account the imperfect connection,

is z = 2.25 10- Ok-1. Air was assumed to be the medium being cooled,

-125 -

- K I

whose temperature ahead of the thermocouple was taken as 3230 K.

The cooling coefficient e is shown in Fig. 37 as a function of the

air blow-through velocity pv for thermocouples of equal height, which

have 25 capillaries with a diameter df 0.1 cm at a temperature of 290 °K

at the cold junctions. As can be seen from the graph, the magnitude of

the cooling coefficient c changes with a change in the flow rate along the

curve, from a maximumnwhere this maximum shifts in the direction of smaller

air flow rates for an increase in the height of the thermocouple. The

distribution of the maximums of the efficiency of the thermocouples of

different heights along one straight line makes it possible to easily select

the height of a thermocouple for a given flow rate of the air being cooled.

" .. ....

Figure 37. The efficiency of a permeable refrigerator

cI as a function of the specific rate of

-44

:•"1 ,o C..",: Ce flow of the medium being cooled pv, .Pvc,. 37. 3a,.1C,1%U'WTh '-qK',1CKTm•. 1

ll1MQt~ P OT V:1e.1M10,lrO J',tCo.%0o•.(,)!•,l~;.o 4 .eiLeUIB .(•:.

The degree of air couling in the thermocouple as a function of the

flow rate is shown in Fig. 38. It turns out that for the same rate of flow

of air through the capillaries, it is cooled to just the same extent in

thermocouples of any height (within the limits of accuracy of the calculations).

This means that the same quantity of heat will be extracted from the air

being cooled in a thermocouple of any height, other conditions being equal

3 However, the efficiency of this heat removal will vary substantially for

various 6 (see Fig. 37).

-126 -(S

' 11

* •.Y7_. . , Figure 38. The depth of air cooling and the

, _I____,______-___ current I as a function of the

Poe. 38. s r'" " oxflow rate of the medium being4 FO .ellM O38 3 '.'X 1I• 7 ,•1 1 OT |VC- cooled, pv

mioaa ox.iwxa:ae.4iOlo Lr-ecmn ":'..

The nature of the change in the magnitude of the supply current I for

a change in the flow rate of the air cooled in thermocouples of various

heights is likewise shown in Fig. 38. The increase in current for a reduction

in height is explained by the increase in the temperature gradient at the

cold junctions of the thermocouple (Fig. 39), thus by an increase in the

infl ex of heat, whose rf.moval requires an increase in the Peltier effect.

In the known circjits of thermoelectric cooling devices having mono-

lithic thermocouples, the requisite heat removal from the medium being cooled

is realized by the Peltier effect at the cold junctions, I = eITI. For

large magnitudes of heat removal, the necessary current is quite significant,

which in turn leads to greater internal heat generation as a result of

Joule heating. The increase in Joule heating for an increase in the current

level (when it is necessary to increase the heat removal from the medium

being cooled) promotes a reduction in the cooling effect. Finally, the

Joule heat can exceed the Peltier heat, and the cooling of the junction

goes over into heating 6].

Figure 39. The influence of the height of the

I ithermocouple y on the nature of the/ temperature profiles when pv 1

-- - ,kg/cm 2 sec.

- 127 -

• -""•'"+" e++" -e' >'. <" '•?++"•+•,:÷ ; :•.:,,:x :•:+,••+, .°••o.;•+-r. .. .

For the case of a circuit having permeable thermocouples, heat removal from

the medium being cooled is realized not only at the surface of the junctions,

but also within the thermocouple over its entire height. Heat is delivered

to the cold junctions only because of the thermal conductivity cU the

materials of the branches. For this reason, the current which is required I

to maintain te given temperature difference at the junctions, as calculated

from (82), will be less than for the usual devices considered at the same

difference in temperatures at the junctions. Consequently, the Joule heat Igeneration conversely affects the cold productivity of the cooling device

(Fig. 40).

. . -- ,, Figure 40. The dependence of the magnitude of the- '5I+., l;'t _ '_:_4 P : : • ' 1 Joule heat QJ on the flow rate of +

• i-.l.• the medium being cooled, pv(.

As is apparent from this graph, in the region of greater flow rates

of the medium being cooled, an increase in the height of the thermocouple

results in a rather significant increase in the Joule heat generation.

However, in the region of low rates of flow, a completely opposite picture

is obtained, the greater 6 is, the smaller is Qj. In the region of small

flow rates, the magnitude of the current grows less sharply for an increase

in the flow rate of the substance being cooled, and in thermocouples with

a greater height, a smaller quantity of Joule heat is generated. This

parasitic heat generation also exerts a substantial influence on the

efficiency of the cooling device (see Figs. 37 and 40). Thus, of the three

- 128 -

---------

4* - 4

thermocouples of various heights which were considered, the most efficient

will be the 3 cm high thermocouple in a range of flow rates up to 2.5 10"5

the 2 cm high thermocouple will be most efficient in a range of 2.5 10 --

6 10-5; and for greater flcw rates, the thermocouple with a height of 1 cm.

Table 3 Ta6.'iuua 31. 2. Hnpoaac•.,. 3. Ioo..,eu 4.

AT. apar) rlapa~ezp , ipu.eCr:po.ec

emax .Qmx 'max i Qaax

e 0,718 0,292 1,04 0.43 Q. 6nz 0,33 0,8 0,31 0.6I, a 9,2 24,2 6.2 15,8

U7 ,m 0,46 2.74 0.298 1.5

S0,216 0,148 0.3 -53 Q. 6nm 0.269 0,379 0.31 -I, a 15,18 22.6 12,33 -W, en6 1,245 2,56 !,032 -

1. AT, degrees2. Parameter

3. Non-blown-through thermocouple4. Blown through thermocouple.

A, comparison of the thermocouples considered here with monolithic ones,

carried out for the same cold productivities, shows that the cooling efficiency

of the permeable thermocouple is 1.3 - 1.5 times higher than of the non-

permeable one. It is necessary to note that these advantages were obtained

for a thermocouple weighing substantially less, insofar as fins were lacking

on the cold side and the weight of the thermocouple was reduced because of the

capillaries.

The influeace of a change in the temperature drop at the junctions on

the characteristics of blown-through and non-blown-through thermocouples was

considered for parallel designs. The results of the calculations for thermo-

couples with a height of I cm and an area of 1 cm2 are ;iven in Table 3.

- 129 -

The temperature of the hot junctions in both cases was 3230 K. The

blown-through thermocouple was provided with 25 capillaries, each having

a diameter of 0.1 cm.

As can be seen from the table, the blown-through thermocouple has

advantages over the non-blown-through couple as far as the power characteris-

tics are concerned.

These advantages lead us to hope that permeable thermocouples will

be effectively employed for conditioning, deep cooling of gases and liquids

in various devices, etc. However, the complex analysis of perforated

batteries having permeable thermocouples and oderating in specific circuits,

requires additional research.

Conclusion

The thermoelectric devices having permeable thermocouples dealt with

in this book can be more advantageous than analogous devices having mono-

lithic thermocouples. Much depends on the operational conditions and the t.function of these devices. For this reason, a comparison of the efficiency

and determination of the practicability of using monolithic or permeable

thermocouples, should be carried out separately for each specific circuit

of a device employed under given specific conditions.

The bases for the theoretical calculations of various thermoelectric

devices having permeable thermocouples are set forth in this book along with

an analysis of their operation for the purpose of attracting the attention

-130 -

of specialists to the practicability of their further, more detailed

development.

For the practical application of such thermoelectric plants, it is

still necessary to solve a number of problems. In particular, the problems

of electrically connecting the permeable thermocnuples, as well as of the

technology of their manufacture from various thermoelectric semiconductor

materials, both in a finely porous and perforated form, has been inadequately

worked out at the present time.

The efforts directed towards these ends at the Institute for Problems

of Materials Processing of the Academy of Sciences of the Ukrainian SSR are

promising, but are rather narrowly directed towards the creation of thermo-

electric modules for a high temperature therinelectric generator.

The choice of the material for fabricating permeable thermobatteries

is complicated by the fact that in practically all of the circuits considered,

they operate in an oxidizing medium. Experiments conducted at the Institute

for Engineering Heat Physics of the Academy of Sciences of the Ukrainian SSR

have shown promise for the application of metallic thermocouples for the

fabrication of permeable thermobatteries. The engineering and economic

parameters of the thermoelectric generatot- with permeable thermobatteries

which was developed and tested here are not inferior to the same indicators

for devices utilized in the cathodic protection of gas pipelines and supplying

low power radio equipment.

A more detailed, comprehensive thermodynamic analysis of thermoelectric

devices having permeable thermocouples will inevitably lead to the creation

of even more economical and refined thermal circuits. In particular, the

-131-

TF

development of multistage thermoelectric refrigerators with permeable

thermocouples for cooling the flow of a substance appears to be

practicable. As the sample calculations show, the efficiency of such

flow coolers will be much greater than the efficiency of devices with

monolithic thermocouples constructed at the present time for similar

service.

Thus, along with the refinement of devices having monolithic thermo-

couples and searching for new, higher quality thermoelectric materials,

it is necessary to expand the efforts in the further investigation and

creation of thermoelectric devices having permeable thermocouples.

132 -

Bi bi iography

.iH1'rEPATYPA

I. Aa 3i T LI p e i 1'. A. iiap. CO-11iniic'n -,epmaoreiiepm~p M0oiw1ocmbio

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.%.0o,:lHTp)Or~lCp2TC~p.- B Hit.: flPeopsaraCOO.oiatc.wetmIIort imalprun~

1 . It p it 0 is Y. A.. K y .1 a r it it A. Pl!. 1-leKoTopue oowpocure.,I03!CrCIII113CCCP.- re.IIIOTCXmIIxa, 1968, 3.

4. 7111 a ItIt e.1 b. -e K B. C., P on r tH c Kc a ItH. C. Tept:om.expo-r.*i!2p1TOpI;. COS113blI3aT. M.. 1961.

5. IIo p a a it zuw it a it E. K. TepIOI~CHTPuMCcKIle CTtlltt11.

6. 1o10 )(!) e A. 4). flO.-)npOUOlIKl3uoL'e TCPN;03.le1NCMIITh1. I I3.',,.IAll C&CP. m.-ZI. 1960.

7. K a it a e 8 A. A.. K o ni it U-. 3. Cy~AODAe It CTa1111to1pitplte xtaukw.

8. V-;-~pnoB B.1'., 'i p it nBcKtii fiB.B.,T a Rit A.A. Ilcr~on.1soliatite TepMOXaMPIIt'iecKttx flOyInPOOUit0.1mBbix KotlitlttIt~olepoll IlarPaiicopTC. Dtieproctia6mci~me ii moiatltuotitupouaiftt UUXIayxa :ta 'rpai-

U. K, 0 T bl p .1 0 r. K. 0 B.1tnsuum1i IIpoý11-a -CMnep,1TYP it Tejo..0.1c0ctt.'re 11a y-CCplefftCt1 %atpIKTCPIICTttK fl0.ayflPOflOXIHitO131X TCp.%I3.1c:d1.-Il f

Toll.- B Kit.: Te:naomcx~i~t'eCKne npoO~ie% ,i nplamoro npc6panonatmnqueŽprint, 2. cdlavfnaaa~yMnap, 1K.. 19701.

10. K o r L, p ai o I' K. Tes!nepalTypttwe noast npit oxa.1aemm -ts enmono. Ac ZTC.ll B ROlp;',iwx it nep~opitpotiattttx crenlax.- B Nil.: Tenao-tjl'31lK,1 It 'Ct1:I0TCXlIt::K, 16. 41 iaviconaa ys;Ka' K.. 1970.

1.K ox -rA p a oaI'. K.. .11 o 6 y i c i 10. 11. 1-kioTopue pc3y.iLTa-.w

na~acttimax.- B it:BonlpOc~ C~IA NIMCCtRofi TCn.(xb13IItll, 3.4 Iayi~owsa!2. K o T ti p , (p r. K., lit c r o a e us r. M. Anaatt3 n.attnimts iip(45AR~ ruTClfcp.ITyp B IIj)OWIMwsC-610t TCPMt0!#eKTP~tt'tWCXOf UN.13Al:.ai.O-

11ur GT31pC 112 CLc 3ollePreTINCiCHIttL Xap.1K~jliC1Itxtt. - Iis

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.ia. -1B Kit.: C.OC;t BI 9lltCl')ItqI~CCNI'X 5 Crauiloixa:.' k c-

. it a c I K it ii 10. 11.. 1 : -, ei LC K an A 1. if"'oc~~m~t..i~l .peeatittnTU1i.100M! 1nfvOKa iIla 4eKMIBstt b o rt Lpi.MhB,1::IP.'.C-

aspa.- B mis.: f~p%.Q6 pdl3,naTC.1I1 CO.itle'liI!"!.3~ seris t.~:sI~

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17. M it .Ia itu o it mi ;I K o Is M1. !A. i A p . BUCOKOUN1e1Culn't) fllf~ft Jim.TO1) - npCO6pa308are.%II tPommm1imap.- ATOM11.11 ýoiieprjisi, 19M4, 17. 5.

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11317apeimlasi3,IX )c IIIC~.- 123B. ISV3013. 3iteprceinK3. 1963, 6.21. 'H it H 0 . ;I c ts 10 -R. it fp C)?0'IKj1IC5flxo.1o.~1iUbiIIK '11-515

ammo~aojls1 cyopoft sicamueoii nomoMums.- ADToTPaKTOPIsoe 9.ICKT-poo6upyaoisassne, 1969, 4. ItWO'irf

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-134-